I'm often afraid I annoy my T. Or my pdoc. Not with emails, because I don't often send my T emails. But in session. I'm afraid I annoy them by not talking a lot, having silences before I say something, not looking them in the eyes or just by whatever I say.

If your T says you doesn't bother her with emails, then you should believe her. If she wouldn't want you to send emails, she would say it to you. And she can decide when to read her emails. I'm sure she has more clients who send her emails. And she won't think you don't have a life, but just that you have a lot going on and T's are the persons you can tell everything to.