I was reading another post and came across this "I feel like I can not ask for anything that is not pre-offered to me"
I think this is another aspect of my situation.

"[I did tell me I could email him and ask if he had any cancellations. I can't quite pinpoint why I am not willing to do that.] I think I don't want to be needy?"
Although I'm not in the same situation, this could be why I don't want to be "caught" (by T) booking appointments every week.