Oh dear, what a nightmare! This is definitely not what a therapeutic relationship is supposed to be!
I fear you are going to have to be the bigger person in all of this and stop the relationship. I am so concerned that your therapist used the word "friend". Therapists shouldn't say that, or even imply the relationship is even LIKE a friendship, because it's not. It's meant to be one sided for the purpose of helping the client.
Rest assured...this definitely isn't you or your BPD diagnosis. This is because of your therapists own issues.
Maybe you could say to her that the confusion around your relationship and her use of the word friend has complicated the therapeutic relationship that you need and you feel you should seek assistance with another therapist?

Definitely a difficult situation to be in....especially in therapy where often what we really want is a friend.