Sorry that your T wouldn't tell you if you had BPD or not. Maybe she doesn't feel comfortable diagnosing you? It might not be personal. Some T's don't want to hurt their patients by accidentally diagnosing them with the wrong thing.

You can always ask your T in your next session, and I would encourage you to do so because I can tell it's bothering you. If she doesn't tell you, you can always ask her why. Can't hurt! Besides, she might offer you some advice on who you could see to get a proper diagnosis.

If you see a psychiatrist, I think s/he is the person you should bring it up to.