Thanks for all of the support and positive comments.
Yes, the hug was a weird gesture, but I didn't really think of it as wrong or in a sexual way. We haven't ever touched before, but she knew I was very upset and I just considered it her way of trying comfort me. We are not in contact at all socially, nor would I ever want to be with her or any of my caregivers.
I sent her a text today, telling her that I would like to have a conversation about what happened yesterday. She is going out of town to visit her mother for several days, and said that she had been in bed with an "agonizing migraine for several hours" that had begun when she turned her head during my session. She apologized to me, not for anything specific, and said we could talk more next Tuesday, which is my regular session.
I have no way to reason all of this out, and it is so odd to me. It all feels wrong. I have an appointment with my pdoc tomorrow, and while that normally isn't a therapy setting, I think I will talk to the doctor about it and ask what she thinks. The doctor doesn't know my therapist personally, but they have consulted on the phone concerning patients, me and others.