Maybe you haven't been seeing your T for long enough to be able to trust her when she says something like this, but it seems like a compassionate thing to say. The DSM is deeply flawed in that it looks mostly at very superficial behavioural indicators. I am much more than my behavour and I suspect you are too.

I have been told by three professionals that I have BPD. I did not want to hear this, because I know it is a diagnosis that carries enormous stigma, and I was afraid no-one would want to help me.
But at the same time, there were moments, when I would read something about BPD that did fit, that I would feel glad to finally have a name for what I have been struggling with for so many years.

In the past year and a half, I have read a lot of books about PD's. I have a bachelor's degree in Psychology from about a hundred years ago, but I feel like I have put myself back in school in order to learn for myself what I am up against.

I haven't kept track of them all, but a very good one is:

Another Chance to Be Real: Attachment and Object Relations Treatment of Borderline Personality Disorder

At this point, I have read a lot about all of the personality disorders (not self-help stuff or "how to handle your BPD relative" stuff, but university textbooks), and I can see how bits and pieces of most of them fit me. The bottom line is that I have some serious problems. How those problems are conceptualized is really not as important as how am I going to overcome them, and who is going to help me.

I think you should definitely talk to your T about your concerns. But I think it will be pointless to try to get her to label you if that is not something she does. I guess what is more important is to ask yourself what it would mean to you if you had BPD?

The most helpful thing I ever read about PD's (and this may actually come from the DSM) is that they are ways of being that begin in adolesence, endure over a lifetime and cause significant distress and /or impairment in work, social or other areas of life.

I was so relieved to know that there were actually enough people like me, who had suffered for years and years without being able to change on their own, that there were books about it!

All those years ago, when I was studying psych, I completely wiped out in one course: Abnormal Psychology. I am not alone in having been convinced that I had just about every problem described in the textbook!! A little knowledge can be a hard thing to deal with!

Whatever you are struggling with, I know for sure that there is nothing 'wrong' with you. But it sounds like you need some help...like me. I hope you will let your T help you in ways she can.