It doesn't exactly sound like you're prone to oversharing. Besides which, I don't think there should really be such a thing if you're working with a good therapist and not using a chiefly behavioral modality. It does sound like it would be a really amazing thing for you to look at your feelings and difficulties around intimacy and dependency in therapy, and enlist your therapist's help in exploring those areas. I also struggle with a lot of shame around the possibility of depending on anyone or being vulnerable. Therapy has been an interesting, challenging microcosm of that for me, in some ways that I think will ultimately be very helpful.

I find that there's a lot of intimacy in my current therapy, and that that intimacy doesn't rely on how much I know about my therapist's personal life or how reciprocal I feel the relationship is. It's about the care with which he attends to my vulnerabilities, the way I listen to what he has to say, the way that he pours himself into the space when there's room and resonance to do so. It's an inherently intimate relationship in a very authentic way, though in my case it's been a slow intimacy. It's difficult, and sometimes confusing, and definitely real.