disclosed major trauma, asked for hug from T

The potential answer is in both of you, which is why you can't know whether or not your feeling should be the basis for an action until you talk about it with him.

Now you're feeling his lack of response to your e-mail is also a rejection and using that feeling as evidence of your conclusion. But again, you don't know the reality of his lack of response, only the feelings you have in response to it.
You can't know what he is thinking and feeling, only what you are thinking and feeling. You're using your feelings as evidence of his intention, but his intention can only reside in him until he communicates it to you--and he hasn't yet.

The fact that you don't have a set appointment complicates things somewhat. You seem to expect him to contact you about an appointment and using that as evidence of whether he wants to repair the relationship. But how have appointments been handled in the past? Most Ts defer to clients to initiate appointments because doing so respects the clients' autonomy. I wouldn't expect him to change that behavior. Since he has responded to e-mails in the past, I expect he will respond, but will probably say that he's sorry you were upset by the last session, and that your concerns would best be discussed within session. He may go so far as asking you to call for an appointment if you want to have that discussion.

Echos, just remember you have a lot you are dealing with right now. Bringing up the rape and everything, having that to process again... just remember sometimes it's easy to repeat a trauma, i.e. this one person took advantage and wasn't there for you so surely this other person will be the same way.

I get being hurt your therapist wouldn't hug you. It takes guts to put yourself out there and ask, but you know what some therapists just don't hug. I think it's ******** too, but honestly I understand why and the reason is they can get sued and potentially even lose their license now a days for something like this. I know many won't especially with people who suffered sexual abuse because the hugs can trigger those bad feelings and memories even if you don't expect them to, it just really is much more of a delicate issue than you might expect, but I know it seems so simple and just human to hug a person.

I know it's hard but I do hope you see this therapist at least once more. If nothing else you can explain to him how his rejection felt and then he'll have to explain himself. I think it might be therapeutic to discuss, it could potentially bring you two closer. If nothing else and he really is incompetent, at least after this next session you'll know for sure and you can walk away without any doubts, and also having taught him something he'll hopefully remember for the next client like you who is sure to roll around. Finally, I think confronting him in and of itself will be a big confidence boost and therapeutic... that's what they say at least. Therapists are good people to practice confronting I think, there's not really anything he can do to harm you, and you are always free to walk away. They are sworn to your secrecy, so take advantage of that ya know !

I hope you feel better soon.

Thanks. In truth I know you are right that I should see him again. Emotions are a powerful thing though and it is hard to resist the temptation to run away. We normally book the next session in session so it is unusual not to have one booked already.
I'm feeling better in myself and keeping myself distracted. Thanks for all the helpful replies

^^ the most succinct and relevant post. It's either one or the other, but not from a place of malice. I think you have a great T who cares immensely about your safety.