Wow, it sounds like you've been feeling disconnected from T for months now. My T and I had a random inexplicable rupture from Christmas to mid Feb last year, and even just those weeks felt like *forever*. It's totally understandable that you would want the relief of clearing it up with her to come with feeling better. You have a lot of closeness to catch up on! But maybe trying to be close still feels risky after the hurt and disconnection of the last few months, and that would be completely understandable too. Is your T usually responsive to you when you reach out and try to be close? If she is, then it sounds like it would be a great idea to take the risk of making yourself vulnerable by telling her how you feel ("I'm sad and I want to be close"), as her response would show you that it's not as risky or terrifying as you thought,
and you'd get some of the closeness you want.
It is not horrible or needy or being a jerk to feel a need to cement the repair of a long and painful rupture with some closeness. Hell, even politicians and presidents who don't really mean it shake hands at conciliation meetings!
I guess this all rests though on what your contact arrangements are with T- if she's not likely to respond (because she generally doesn't, not because there's anything wrong with contacting her this time) then this would reinforce all your negative feelings about yourself and her. Are there other ways you sometimes use to feel close to your T? I sometimes make mine something, or go somewhere we've talked about, or take photos to show her, but maybe you'll have your own tried and tested ways?
Thinking of you