Hi pikenbass. Welcome to Psych Central. Glad you have been so responsive to your girlfriend's recommendations to pursue therapy with a therapist (T). I am sorry you assume that DBT is for borderline personality disorder. In fact it is used in treating many mental illnesses. Here are some of the books that talk about different applications of DBT.
http://tinyurl.com/mrdxvdl
So your T sounds like they don't just want to have you talk, they are trying to give you coping tools. Here is an article about DBT and what it offers.
https://psychcentral.com/lib/an-over...therapy/?all=1
After all I heard from other people and their experiences with therapists, I think you are fortunate to have a T that wants to help you learn tools to cope with the challenges you face. That is quite supportive. Maybe you could ask the T what workbooks would help you, so you could work on them in between sessions.
In my opinion, to keep changing T's whenever things get seriously looking at solutions, could be a sign of evading the challenges. From what you said about your girlfriend, that might not be interpreted as a good sign by her.