I don't think there's such a things as TMI in therapy - as in I don't think we should feel that we shouldn't share things we want to share because it's TMI.
But, as others have said, that doesn't mean everyone is ready to share everything all of that time. Or even that it would be helpful for them to do so.
In some cases - but definitely not all - I would say what you're describing *could* be a form of avoidance. But even if you *are* being avoidant, I wouldn't attach any judgement or criticism to that ie avoidance isn't necessarily "bad and wrong".
For me, avoidance is one of my key defence mechanisms. Avoidance, denial and dissociation - all three make therapy very challenging and frustrating for me because they kick in (usually when shame is present) without me meaning them too and then I am gone and it's game over - we can't do any more work and it makes for very slow progress. I beat myself up about this for a long, long time and sometimes still do. But I have generally come to accept and respect that our unconscious defences are there for a reason - self-protection, generally. And, in my experience and according to my therapist, you can't really just force your defence mechanisms to stop/move aside Just because you or your therapist wants it to.
If you are deliberately being avoidant then, sure, you have more control over whether you choose to keep avoiding it or whether you choose to push yourself onwards and through it. Even so though, I would still argue that if you are consciously, deliberately avoiding stuff, there is a reason - and perhaps more than one reason - why you don't want to go there.
Personally, I think it is very useful to try to examine (with your therapist, on your own or with people here) our avoidance/resistance to find out what's underneath it, what it's for, how well it is serving us (or not!).
I don't think it's useful to be punitive about it - for your therapist or for you to give you a hard time about it not being helpful or there being no place for it in the therapy room etc.
If your therapist hasn't come across people avoiding things with her before because they feel embarrassed or ashamed or afraid or whatever else, I am stunned. I would have thought a therapy room is a very common place for it!
As for what has helped me...
As an unconscious defence mechanism, avoidance is still very strong for me and I'm not making much headway with that at the moment.
The deliberate, conscious, feeling too embarrassed and not knowing how to go there though...If there are things you do really want to share and feel ready to but you feel too embarrassed to get the words out in the moment in front of her or you don't know how to bring it up...
You could write it down and email it to her/hand it to her in session/read it out to her in session. That can sometimes help. If I'm about to share something that I think it embarrassing, I will often name it and say something like "I want to say something but it's embarrassing and I don't know how to say it..." Any good therapist would then help you with expressing it. I also sometimes ask my therapist not to look at me and she is fine with that and very discreetly looks away and then often the shame feels less intense.