Is your T asking you a lot of questions because you are not talking? I think it is quite common for the T to let the client lead the session. They let you choose the topics. I think with clients who won't talk, sometimes the T falls back on asking questions. Other Ts fall back on allowing silence. I think the question strategy can backfire because then the session ends up not being about what the client wants to discuss. The silence strategy can be frustrating too, in a different way. My concern with what you've written is that you did try to tell her something important and she didn't want to discuss it with you: "I told her I was shaking but she just dismissed it". You also wrote that "I get the sense from T that I need to keep it light". Both of those things are concerning. I think you should discuss those things with your T, because they seem to be impeding therapy. Maybe you could write what you need to discuss on a piece of paper and hand it to her, just to get the ball rolling.

My sessions sometimes do include chitchat, but I know that if they do, it was because I chose that. My T is ready at an instant's notice to jump into the deep stuff with me. It just requires my courage to ask him or bring up those hard topics. For me, I think the chitchat can be a way to avoid talking about what's important and difficult.