Crush - keep trying or let go?

So 22 year old male here.
I go to a GYM a few times a week, and sometimes I see this young woman to whom I felt an attraction on sight.
The first day I saw her, I slowly came to her and ask her name. I said mine afterwards and gently shook hands with mutual smiles.
Second time I saw her, I small talked with her a bit, it was fine.
Today I saw her again and wanted to engage more.
I was doing a kettlebell exercise, and during the middle I decided to come over her and ask her if I can give her company. She gave a partial node, and I kept my talk as smooth as possible - I was vibrating with excitement/anxiety, especially my face, so it was kinda difficult to talk, but I did my best to keep smooth. I told her about how "deadly" my current exercise is to empathize with her always-tired looks at the gym, and asked her if she wants a piece of my energy bar. She said she has already eaten, but I just nodded because I was too excited to have a lasting conversation!
I then had one of those "slips" when you get excited from a crush - I landed on a pedal of one of the machines, so awkward moment. I looked at her in positive shock, smiled to myself and started doing my exercise near her.
And here is a red flag - she went away to a different station (she just started the one she was on previously).
I didn't chase her, I stayed at my spot and moved on to my other stations. The one after the kettlebell was another leg exercise station. By coincidence she came and asked if I'm exercising there. I told her yes, and asked her if she wants to go first. She nodded. We switched place, and then she switched with me, I even readjusted the seat and leg pole for her. She said the seat is not right and asked for help. I helped her, and insisted that I take it more back than forward. I did so.
I tried to ask her a bit about herself - how old she is and what she is doing right now (work, university, etc). She didn't hear or respond to my question during those moments because she insisted on adjusting her station. After she finished - wandered to the previous station.

Whenever I talk with her, she sometimes seems irritated when I talk with her. And when I talk with her there's no small-talk kind of talk (I don't know how to call it) like she has with the gym trainer who's always there when she's there (he's middle-aged, so it's just platonic). But it's not all irritations, she does answer fine, sometimes smiles. She did node when I asked to accompany her. And sometimes I even catch her glancing at me.
Today when I left the gym I told goodbye to the trainer, a person I met and hesitated whether or not to say bye to the woman I met. I went on my way, looked at her and she was back-faced. Walked again and looked at her. She happened to see I'm looking at her (through a mirror probably) and wave goodbye to me and immediately told and waved her goodbye, too.

It's been 8 hours, I wish I could write it the moments I came back home but I had to go to work since by then I remembered more details.

So anyway, I sensed red flags, but there's a part of me which is still in question.
She always seems tired and I sense that so I ask her "how's it going?", "you okay? you seem worn out!", "do you want a snack bar to boost you up a bit?". She's always insisting that it's ok, that she's not tired (I feel otherwise (but still want to believe in her (if she gives a chance to get to know each other))).
Also that women are generally introverted so there's no clear idea of what is going on inside her (learned from my own senses and experiences of course, I'd love to learn if I'm wrong).
The last thing I want to do is irritate a woman, it's kinda devastating me a bit when I see such red flag signs since all I want is to get to know and perhaps develop a path towards a loving relationship.

I'd love to hear for advice.

Thanks!

Sorry, it was difficult for me to follow the details. What are the red flags in few words? Do you mean that she seemed irritated from you talking to her?

Women are generally introverted?

This statement is false given that the majority of people are extroverted.

I don't think you are using my this term correctly.

Introverted-----re-energizes through alone time.

Extroverted-----re-energizes through contact with other people.

But in general, many women are irritated by guys who hit on them at the gym. (It's a BIG reason why women only gyms exist.)

I also don't think you understand what a red flag is. A woman not giving you 100% positive feedback is not a red flag.

Red flags are more along the lines of "he won't tell me where he lives even though we've been dating for three months" hence a red flag of the guy being married! (For example.)

If you interpret every little thing that didn't go perfectly as a red flag, you will be single for life as you'll end up misinterpreting actions and throwing people away for no reason at all.

ok, so instead of red flags, I'll call it subtle signs, since those are subtle signs - they either mean little or nothing.
As for the bold, that's exactly why I still have a feeling of optimism about her.
What do you suggest I do? From the subtle signs she gave, I don't feel she's really into this. It's in a way unpleasant for me to talk to someone who seems irritated from you, especially if you intend well. Do you see things otherwise?
I'm thinking of moving on - not away but not forward either. I may greet her, throw some small talks only if more possible. And that's about that. The most important thing for me is to keep things cool and fine.
But I still want to hear your thoughts.

Mr. Stranger - the "red flags" I referred to are the irritated looks and tones, going away from me when I went to be with her and when we worked on the same station. However it's not all "red" as I've mentioned.
I'll fix it to "subtle signs" instead, because GoldenWaves has a point about "red flags" relating to more major concerns.

Don't OVERTHINK all this, you just had a few words and she didn't tell you to go the hell away.

I get your excitement but keep it in check if you see her again . You don't want to come on yo strong.

I agree, these aren't red flags. I'm not sure, but I think instead of keep talking to her in the gym which might be seen as intrusive, why don't you ask her out in an appropriate moment, and give her a space in the gym to exercise? Just a thought*

*Think twice before you consider my suggestion

Hi Vibrating Obsidian: it is hard to tell from your post whether you are having difficulties with English as a second language or are being too naive. Your generalization about women being introverted and your assumption that the middle-aged trainer is platonically disposed towards young women both sound naive, but at the same time I sense that you are struggling with your usage of English and that you might be quite sophisticated in your native language. Whatever it is, I agree with Christina's advice not to overthink it and just go with the flow. You cannot really get this one wrong. At worst, it won't proceed anywhere. At best, it will. There is no danger in it for you.

With best wishes.

I would say leave her alone while she is exercising. I joined a gym a few years ago and guys turning and staring or taking every chance to compliment just made me angry or uncomfortable.
She is there to exercise, so talk to her at the end or invite her for a drink so you will know how she feels about it.

I've acknowledged everything you wrote.
But I end up sitting here in front of the computer... it's hard for me to reply.
The whole topic of a relationship with a woman goes deep down into my heart.
A few tears dropped.
Is it ok if I open something more deep and personal about me and women? It's something in my heart...
I have some women anxiety regarding being so open, but I feel it can greatly help

Sure. Open up. I will listen and see if I can help.

@ Vibrating: don't beat yourself up, there's no perfect way in life. I think the best way is to stay kind and polite. Anyway better try than nothing

It would help a lot if you open up, since your post hints at that women anxiety, but does not talk about it, leaving the readers unsure as to how to best advise you. It is better to tell the whole thing.

My heart yearns for a woman's compassionate heart.
I want to love a woman for who she is.
I wrote about it in some threads here, about me and women.
I'm working on feeling comfortable with whichever woman I meet. I'm working on overcoming feelings that women are cold, selfish, etc. I just don't wanna say such words anymore, it hurts my heart.
I feel that it can be like I once feared dogs - I feared them greatly, but after I got a dog at home, I started loving dogs like crazy!
I want it the same with women!

Sad Mermaid - I'll say it openly. When I first read your post, I got an impulsive negative reaction - "how could she say I'm bad at english and naive, as I wrote my post late at night with so much details to remember. My English is fluent as I consume English media on a daily basis, more than my native language". My first reaction was as if you're judging me. But then I told myself "Wait... look, she's trying to help you. She's saying all this for you. There's absolutely no point in making this the topic, just hold it in and know that she is doing this for you. Scales of qualities don't matter, because you know your worth, and that this is not what you need to settle with her. She's helping you out, that's a very positive thing, that is the light... "
So I'm turning what seemed negative, break that harsh barrier to turn it into a great positive, and giving you big thanks and a sincere hug for your very kind help , you deserve it

Today I went to work and felt much better with myself. There are customers and sometimes they are women, and I just loved appreciating the small moments of attention from them. There was even a woman who ask me some questions in a gentle whispering tone (which I really liked) and felt a chemistry in our talk, I saw and felt her smile and it was a very beautiful moment, her smile was so touching and beautiful!
And I also talked to a co-worker, we talked about admissions test we will both take and it seemed we complete each other in what each of us excels and has difficulty with in the test, so it was an entertaining moment to offer mutual help and she agreed, got her phone number and I even asked if we can walk together after work. I feel so satisfied from out starting relationship, whichever it may be, so long as it's all positive I'm highly satisfied!

Also, I want to break my barriers by thanking all of you women who have also helped me out. When I made this thread, deep down I wanted answers from women since I want to break my anxiety so I can love listening to women. I loved getting attention from you.

There, I said it

Edit - I started feeling anxiety in my heart after posting this. An anxiety which masks the love I have expressed, the love which only wants out. But I'll listen to you more than I listen to myself now.
I'm all ears... and heart.

Vibrating,this woman at the gym just sounds distracted and maybe she is there to exercise only not to find a boyfriend.I think the way you behaved with her was good,and now backing off is a good idea too.With women you can be too attentive and that usually puts them off,playing it a bit hard to get and not so keen works better.You know the saying people don't want what is readily available they want what they can't have.Hold back a bit to make her do the running towards you,so then you can discern if she is into you or not.This is more general advice than specific to the gym woman but equally aplies to her too.I mean you did ok and are doing ok ,don't worry or beat yourself up.With time and practice you will find yourself becoming more confident.Make sure you are addressing those negative feelings about women being cold and selfish too and finding example of women caring and warm to see women aren't all bad and that you don't need to be resentful otherwise those shadow feelings can come out in you when you least want them to or expect and can ruin something for you.But try not to overanalyze situations, you are doing good as far as I can see!

Thanks Marylin, you're very sweet

I'm really not sure where you get the information that women are generally introverted. Just the same men are not generally any certain way either. My proof is in that all the women I've been with are more extroverted than I ever will be.

From all the details though, it's really hard to say whether she's interested or just being friendly or polite. Your interpretation that she seems 'irritated' could be perception or otherwise.

I don't know, though at this point if she's not willing to make small talk that could be a sign she's keeping it at the acquaintance level but none of this is cut and dry.

From personal experience though years ago, when I was at the gym to work out, I usually had another schedule I was trying to fit it into so I needed to focus on my exercise which didnt have ANY TIME to socialize. I would acknowledge someone I interfaced with for whatever reason it related to me exercising but nothing beyond that.

Honestly I did my most gym socalizing playing racquetball with the guys. I especially enjoyed the challenge court because while waiting for my turn for the challenge I could socialize with the others who were waiting too. Have to admit not many women were up to the top players that played the challenge court..i was the only one at times but thats when I got to meet other guys to set up games with also. Not much socializing on the court but there was more connection made given the competition & the acknowledging good shots. Enjoyed the racquetball interface much more than exercising which is individual & FOCUSED.

I wouldnt push anything with women. Simple little connections great. If you run into someone on their way out & can struke up a conversation on the way checking out or heading out to the car, that would be much more relaxed & better accepted unless they are in a hurry...be sensitive to the person you talj with

Vibrating Obsidian: thank you. Are there any other women on your horizon?..

Not right now, as my only social settings are work, the gym and occasionally going to bars with friends.
But I have been going hard on myself lately. I feel taking it easy, yet appreciating every moment I communicate with a woman will both help and satisfy my heart.
I feel my anxiety regarding this won't be dissolved in one night as I still feel some anxiety after writing here.
But I'm glad I can bring this all up.

I think every rational individual would agree that positive changes would occur in your life little by little.

I think Sad Mermaid commented on the language barrier to confirm that it was truly a language barrier and not that you are very naive so she knows (and we know) what kind of advice to give. If the matter is simply the difference of being native speaking or translating in one's head then the advice you'll get will be one way, whereas if the reason you refer to things the way you do is because of being naive, then you would get different advice.

I do think you are young and have a lot to learn about women. I think this woman at the gym does not sound interested. I would back off and leave her alone. I know when I'm at the gym I just want to work out and not be bothered, not stared at or hit on. If a guy talks to me at an appropriate time, I might be open to it, like when I was getting a drink from the water fountain or stretching, but not while I'm actively at a station trying to focus on my workout.

I would back off if I were you.

Good luck,
seesaw

Update - perhaps I have a new crush! She's a co-worker.

I'm having some mixed feelings and thoughts about her.
She's a very friendly and playful person when interacting with men. However I sense she's the kind of "daddy's girl" kind of person because she's going abroad with her father, so she may be a little oblivious to romance, but she's so cute and we have a great conversation chemistry. I also feel I have some feelings for her, yet I feel she has some insecurity about men, so I'm not sure if going "strong" or "direct" is the right thing to do.

Here's the story:

Yesterday we worked together evening.
She mentioned Valentine's Day and about how we'll all spend valentines day alone, yet how being single is an advantage kind of small talk.
I didn't say anything, other than feeling an impulsive "now's my chance" feeling.
But I talked to her as usual during work and breaks, getting to know her, listening to her, talking greatly as usual. I let her drive me near my home to be with her for company and offered her to show me the pancake restaurant she mentioned today sometime.
I offered tomorrow, but we can't, and she's going abroad for a week this weekend.

I personally don't make such a big deal about Valentine's Day, but I have this exciting feeling of wishing her a happy Valentine's Day and that my offer to go to the restaurant was a date offer or something.

Although the thing is, because of the insecurity I sense and the fact that she reminds me of my last ex who also had a juvenile behavior, I feel that I need to take it slow. It's only because it's Valentine's day, and while I personally don't make a big deal out of it, my heart tells me it's a kind of a "stars-align" day.

What do you say?

From all this writing and overthinking I just told myself "You're overthinking(/feeling), so relax a bit and wait". Still want to hear from you all, though.
Thanks for the support!

Focus on reality not emotionally charged crushes. They usually just complicate one's thinking. If a relationship happens with someone you are attracted to great..if not....oh well it wasnt meant to be

Yeah, I prefer to let the feelings get mixed into a cocktail I call "conclusive feelings". Conclusion - She's cute and I have a little crush on her. She's really sweet. I went out with friends today and contacted her on messages. Was driving and when I saw a notification from her on my padded phone, it gave me a happy warm feeling in my heart.
I just need my anxious feelings calmed and probably take things slowly. There's no hurry, I know she's a sweet person I'd love to get to know more. Writing that makes me feel even fuzzier inside.

Also, what do you exactly mean by "emotionally charged crushes"?

I find it a little troubling that you say you're interested in her yet you've made negative stereotypical assumptions about her. You've called her a "daddy's girl" because she is going on vacation with her father, you've called her juvenile, and you've said she might be obvlious to love/romance. Most women would not be interested in dating a guy who talked that way about them in particular, or women in general. You are making all these assumptions about her without any justification-- and all of them are negative stereotypes. You might want to think about the way you perceive women and why you jump to these conclusions before trying to pursue a relationship. Most women want to be respected by a partner, not infantalized. She might be playing up the "single us great!" line because she has already figured out you have a crush on her and is trying to politely give you the hint that she isn't interested romantically.