Struggling with Self-Diagnosis and Labels in Therapy

Honestly that sounds like kind of a red flag and I would suggest a second opinion, I dont mean to sound harsh and she may be a plenty good therapist in other aspects and some people do have issues with labels, but diagnoses can be a pretty important part of recovering and bettering yourself especially if you're struggling with something that needs specialized treatments that are walled behind a diagnosis or further knowledge from a professional about your symptoms to figure out coping mechanisms. Labels and diagnosis might not be for everyone and that may depend on the specific label but that doesn't mean it's not helpful for many others. It's also not a great sign that you feel like you can't tell her these things considering they're related to your mental health and is clearly an issue for you. Plus if BPD isn't her specialty and she doesn't know much about it, it might be a good idea to get a second opinion from someone who does, even if you decide to keep seeing her afterwards.