Have you expressed to your T that you're feeling overwhelmed in session? Because you're right, that would definitely make it more difficult to share things that you feel are important.

Your T saying "it wasn't important," isn't quite right, but I've had experiences similar in my sessions. I walked in one time and said something to the effect of "I have so much to talk about and don't know where to start." My Ts response was, "well, what feels most emotionally pressing right now?" Not that the other things weren't important, but that I was most affected by what we ended up talking about.

I don't email my T, no. I've texted him once, but that was in a semi-crisis moment. I've never discussed out of session contact with him, so I don't know what his boundary is. The no contact thing is a Daisy boundary. I don't want to become too reliant on any T.