DID will almost always include periods of amnesia. Try making a timeline for yourself, and for each year, list out as many general memories as you can. If you notice some huge gaps, it might be a major sign.

BPD is a very reactive disorder, and will mostly affect your personal relationships - usually the more emotionally intimate the relationship, the more severe symptoms can become. But it won't make you have periods of amnesia or blacking out.

People with BPD have a weak and confused sense of self, because they are groomed and conditioned from very early childhood and onward to 'be' whatever their caregivers want them to be, typically in a futile attempt to get their emotional needs met from very abusive and unpredictable parents. Their sense of self 'doesn't matter' and is so aggressively invalidated that it never gets the chance to actually develop all that much. Combine that with splitting issues when it comes to perceptions of other people and one's self, and identity issues are pretty significant.

But this is not the same thing as the brain creating amnesiac barriers which wind up manifesting as a fractured mind, in which different emotions, memories, etc are completely cut off from each other, creating the subjective experience of having multiple personalities inside the same mind. This is why amnesia periods can be a dead giveaway of DID.

Also your therapist sounds like an idiot and a coward. BPD is heavily misunderstood and stigmatized even with the professional psychology field, and some therapists are so unwilling to work with people with BPD due to the stigma that they will sometimes just flat out go into denial about a client having a personality disorder. If he was worth his salt, he would have asked you how you felt about the diagnosis, what symptoms you experience, what makes you think you have BPD is you do believe it - you know, actually do his job as a therapist. He doesn't have to believe you have BPD, but he does need to know what you think/feel about it and why in order to do his job.

I don't want to tell you what to do, but those are my honest thoughts.