Hi Middlesister,
Welcome and hello
It's good that you're doubting what doctors are saying, listening to your own intuition. Have you read Blaise Aguirre's book about BPD and adolescence? He is a leading expert about BPD in teens and has a lot to say about the goofiness of not diagnosing people before the age of 18, like something magic happens on your 18th birthday. I would go get that book immediately and read it cover to cover, there's a lot of really helpful and up-to-date clinically researched information that will give you hope.
In the book Buddha and the Borderline, the author finds out over a decade later than she was diagnosed BPD as a teen, but no one told her or her parents. If nothing else, it will convince you to advocate for your daughter getting the right diagnosis.
If you do get a diagnosis, the treatment is often dialectical behavior therapy to help with distress tolerance, reality testing, emotional regulation. It's sort of like cognitive behavioral therapy (CBT) with mindfulness skills, and was developed by Martha Lineman, a psychologist/researcher who suffered from BPD herself.
My partner's daughter was diagnosed bipolar II after experiencing a psychotic depression at age 16. I am convinced they missed the dx, or else did not want to tell her. I'm not her bio parent so feel it is not my place to say anything. Your D is lucky that you are listening to your intuition on this. Trust that voice in your head. The worse that happens is she receives the same treatment that can help her with the other diagnoses you mention -- depression, anxiety.