Your T isn't going to think you're a slut. Mine didn't. If there's anyone who's going to understand that you're not doing this in order to have a grand old time, but rather because you are deeply hurt, confused, and unable to cope, it's your T. Don't worry too much about how you present yourself... T knows you're suffering. And has plenty of experience with bad coping mechanisms. Mine was very much able to be compassionate without excusing any of my behavior, the same way he would have been if I had instead been drinking until I passed out every night after work, rather than cheating.

I'm glad you're already trying to process why this is going down the way it is now. That's exactly how you're going to get better.