Hey!
You know, the whole issue with mood changes, then moments of confidence, then being irritable... I completely relate to you 100%.
I believe you. I have had the same problem for a year and a half. I know what it is like.

I would definitely advise you to go see a psychologist/therapist. These problems with mood really contribute to concentration etc. like you described, and it can really mess up your day and get in the way, making certain things difficult.
I really think it would benefit you if you went at least for one session to check. I'm sorry to hear your mom might really doubt you, and I get where you are coming form when you say you are worried the therapist won't believe you. However, I would have a go at this, and if your mom doubts you then justify it by saying that it really has an impact on your everyday life, and it makes certain things difficult.
Tell her that you would really prefer to go and make sure you are okay, or maybe to identify the problem if there is one, so that you can solve it. You should tell her how you feel about it and how it would make you happier if you went. You could even bring up that you were diagnosed with anxiety before, and it is possible for you to have some sort of mental illness, so you would feel more secure if you could go and check if this really is a problem.
It doesn't necessarily have to be something serious or big, but I'm sure there is some way to help fix it.

As for the psychologist not believing you. Since they are a psychologist, it is their job and responsibility to completely hear their patients out, and to not judge or make assumptions that they are 'faking it' or something like that. I'm sure that whoever you meet, they will listen and try their best to help you out.
It's worth a try.
The symptoms you described seem legitimate to me, and even if they are not, you could still ask the therapist to give you advice or maybe some small medication to help you with concentration or moods.

However, I understand that you are nervous and worried about it, so I don't want you to feel like it is the only option for you. Who knows, maybe you can find another way to hep yourself concentrate, boost your confidence a little, and make yourself feel happier. It's your choice and your decision; have a think about it. Whatever makes you teh most comfortable.

(Sorry if my writing may seem a bit chaotic, I sometimes type really fast and try to put all my thoughts down into writing as fast as possible).

I hope that you can soon feel confident to make the decision, and have a shot at it. Good luck