Hi Retro,
Lots of times when I read your posts I feel like could have written them myself. I too was convinced I had BPD, and like you, my T wasn't hung up on a diagnosis, but rather my symptoms. I eventually asked to be officially diagnosed and went through a formal assessment. Turns out I have a whole host of diagnoses, but the way we did therapy didn't change. My T did bring a few new things from DBT, when I expressed the place we were at wasn't working for me.
Maybe you can talk to your T about different approaches if she's reluctant to name what you're dealing with - if that makes sense.
I hope the new meds work. Good luck.