Some therapists are not into diagnosis. My therapist, for example, approaches the client from a position of health rather than pathology. He has never felt a need to put a label on me, and I haven't asked him for one.

I would give your therapist a chance and let things unfold naturally. If you share some characteristics with people who are labeled BPD, he will know after a few sessions.

I think it is great you are trying therapy before automatically jumping to meds. Hang in there. Wishing you good health. And good luck with your therapist! Just be yourself, and be honest.