No it is not normal to be treated that way at all. Forgive yourself, for feeling down about being "dumped" by a friend and being blamed for her leaving. TBH it was her choice and from what you've said she did her share in making the relationship unhealthy. She put you in second place by changing plans with you so often for her other friend. Anyone is going to feel the sting of that whether they have bpd or not. Her saying you overreacted, well I can't say for sure but I do know part of that is her pride, hiding the fact she did not want to face up to the fact she wronged you at all so she deflected onto you and redirected the focus on your reaction rather than what you were upset ABOUT.

Nothing in what has happened has pointed to you being worthless, horrible, a bad friend or any of the plethora of things you can think of to defeat yourself. I'm sure you did some part in the whole relationship problem but there is no way it is because of your worth. Trust me on that.

We BPD people take too much of the blame and we don't question it. We need to. We need to look at the fact that we have only part of the responsibility for making a relationship work. The friend, lover or family member has theirs too and the tendency is to pass it all off on the bpd, because we're easy targets.

Don't let yourself be. She sounds like she was a sh*ty friend.