I really feel for you. What you describe is familiar and horrible. It really does have to be worked through, though, and I promise that the relationship on the other side is worth it.
May I ask the professional level of your therapist? I ask because it's troubling that she would say you "might have BPD." I'd want to find out for sure, because the therapy should adapt to the diagnosis. For example, many, many people with BPD also do DBT (Dialectical Behavioral Therapy)--in fact, many therapists won't see borderlines who aren't in DBT or who have at least had it one time through. If you haven't had a formal eval from at least a psychologist, then it's probably time to ask for one...
The extreme attachment and the fear that the pain of it will eat you up sure sounds like my borderline experience...I go through phases of the "this is so painful I can't stand to be here--as horrible as it would be to never see you again, I can barely stand to come to a session." Recently, I had a really awful bout of them. Repeatedly, we work on creating social ties with others in my RL, and we work on creating boundaries for myself as well as recognizing the boundaries of others--for instance, I would never/should never tell anyone else all the things I tell my therapist; and if I DID tell a person those things and it was not a loving, committed relationship, I would be violating my own boundaries and heading for trouble...and I should wonder why that other person wanted to know so much about me if they didn't love me. Make sense? Lots of