I definitely feel "dirty" and guilty about my emotional wants and needs, including intimacy. I worry about being "too much" for my therapist or the idea of him recoiling in horror/disgust if he knew the extent of it.
So the first thing is you're not alone and you're not doing anything wrong by feeling this way.
How your therapist responds will depend on a lot of things. In general, psychodynamic and trauma focused therapies are going to be more intimate, whereas as a CBT therapist will be less focused on or possibly even uncomfortable with a large degree of intimacy. It very much depends on the individual therapist, of course.
Being able to broach these subjects and not shock/horrify/disgust my therapist has been really important for me. My feelings about my own wants and needs and shame have been major contributing factors to my issues and my inability to treat myself kindly.

I recently brought up my inability to make eye contact with my therapist, especially when talking about topics I perceive as shameful. I asked if he was relieved that I didn't look at him and he said no, that he'd prefer to be able to make eye contact with me. I told him about feeling like I shouldn't be allowed to have that, that I was disgusting, etc.
He said he'd like for me to try to make more eye contact then to challenge that. That he wanted me to believe that I was worthy and deserving of that kind of intimacy.
Eye contact was a way for me to have a conversation about one aspect of emotional intimacy without addressing it directly, and it helped me feel out the situation and get reassurance that he was comfortable with it, even though I'm not.

Talking to your therapist about it is the standard advice (and usually the best advice) but it's not always easy. Finding a way to gauge your therapist's reaction before jumping into the topic can make it easier.
And if your therapist is more detached and not comfortable with emotional intimacy and that's something that's important to you, there are plenty of therapists who are.
Emotional wants and needs and wanting intimacy are normal and okay and not shameful. Experiencing those things intensely is especially common for those of us who didn't get those needs met in childhood.

If this resonates with you, I highly recommend the article Attachment to Therapist: A Primer
I've recommended it on here a few times before because it resonated with me so much and it made me feel less abnormal and ashamed. I actually brought some parts of it printed out to a therapist appointment to share with my therapist because there was a lot of it I couldn't bring myself to say aloud. My therapist was more accepting and understanding than I could have hoped for.

I hope you're able to talk to your T about it and that it goes well.