It's okay whatawhat. She's not demanding that you do this now. It sounds like you are hard on yourself about how difficult this is. Did you talk with your T about your fear of crying? Let her know so she can help you with that. It might or it might not happen that way.

It's okay to be scared and to tell her about being scared - that is the first step toward talking, and this IS a deep issue with you and is impacting you right now.

I sometimes feel like I'm not talking about things that are deep, and when I talk about that with my T, she assures me that we are and tells me why it is deep. It's very encouraging.

Keep saying to T whatever comes to mind, even "I'm feeling scared right now".
Let her help you with it. That's what she is there for