I do this a lot too, sit and say nothing, even though my mind as constantly chattering away. I make sure and wear nail varnish just so I can pick it off. Can you ask your T if you can write to him/her, you could find that easier? I have a problem talking to her, or generally talking about difficult things without crying so maybe writing it down what you want to say might be of some help.
Btw, if your T is getting frsutrated, I would look for another one...its their job to be patient and gain your trust so you will feel safe to open up. I always say sorry to T after a session where I sit in silence and she always says "Button, its ok, no need to apologise, this is your time to spend how you like with, if you want to sit there and scream its fine or sit in silence thats also fine..just know that I am here and supporting you in your choices...she also says that I can email her something if I found it difficult to say.