Couple things:

Your mom is out of line. That’s super invalidating and triggering behavior for people with BPD. Regardless of her intentions, she’s making the situation worse than it is with her careless talk. Someone needs to send her the memo (your dad? A relative you trust? Psychologist that diagnosed you with depression?).

BPD isn’t diagnosed in anyone your age. Your brain is still developing. You’re still learning what behaviors are/aren’t okay—you’re a minor. Like, it’s important if you’re being actually diagnosed to not misdiagnose people. That causes a lot of damage, especially in a condition that is so highly stigmatized.

What you can do is ask to attend therapy, and literally tell them this exact story. That it’s your mom telling people you have this condition and it’s making you question things. They will be more equipped to properly guide you through what you’re feeling, what’s valid, and most importantly give you accurate information on your diagnosis.

For real, your mom needs to shut up.