If it's okay with them to email, that seems a good idea. Or maybe type something and bring it to session so T could read it with you (better able to have her reaction and 'live' interaction, so to speak). Maybe you could write something as in (only if that's what you want) maybe she could gently prompt you or help you to open up.

I don't think you need to apologise though. It's hard to open up anyway. But yes, if you could get her on board that wouldn't hurt...