Maybe you could bring this up with your T - ask him if he can give you some space in session to process things, or some way to communicate with him once you have processed the session. One of the things I really like about my T is that she's an introvert like me and understands that I need to be able to stop and think about things and process what we've talked about. If there's a good point in session to allow me to do that, then she gives me the space to do so. If there isn't, then I'm able to email my T after the session, once I've had time to process things. My T understands that emailing her is my way of processing, and we usually talk briefly in the next session about whatever I emailed her.

I do bring my journal to sessions with me, because I feel more comfortable communicating in writing. However, my T usually asks for me to read my entries out loud to her. She has never taken my journal and read it herself, even though I've asked her to a few times, when I thought the entry would be too painful for me to read out loud. I choose what to share with my T, and I can read as much or as little of an entry as I want to.