Hi BetterDays,
There are some doctors who will diagnose adolescents. In fact, McLean Hospital at Harvard has an adolescent unit. But unfortunately because of the stigma the diagnosis carries a lot of doctors are reticent to diagnose it.
There is a book I read when my daughter was younger called Borderline Personality Disorder in Adolescents that i found very helpful: Borderline Personality Disorder in Adolescents, 2nd Edition: What To Do When Your Teen Has BPD: A Complete Guide for Families
https://www.amazon.com/dp/1592336493/ref=cm_sw_r_cp_apa_i_Ckj3BbEASXW53I can really relate to what you're going through. We ended up letting our daughter try online school because the social environment was so stressful and distracting for her. She didn't really actually do anything but she did get her GED, which might be a route you want to look into. Our daughter passed the GED with basically no studying. She too was failing every class.
I'm glad she'll be starting DBT. Our daughter unfortunately has refused any treatment and she is now 21. If she is able to take dbt seriously it will probably really help her. I think without a diagnosis you may still be able to insist she get treatment because I'm sure it's obvious to her that something is wrong. Several books about BPD describe it has having no emotional skin and being the equivalent of an emotional third degree burn victim. That is no way for anyone to live and I hope your daughter will be able to see that her emotional volatility is very stressful for her and reduces her quality of life.
Something else that I've heard people do is give the person they suspect has BPD a description of it and ask if they can relate to it. Many people feel a lot of relief when they can identify and name the thing that is happening to them. You might want to look for a video or description written by someone who has BPD rather than a clinical description. I think it would be easier for her to relate to.
I hope you'll keep posting, we are here for you