Whether or not the diagnosis is BPD, CBT will help. Indeed, it is particularly helpful in preventing relapses in BPD, though in that condition it is almost always used in combination with medication. BPD is at the psychosis end of the diagnostic spectrum, hence the need for medication, as opposed to neuroses like anxiety and reactive depression, which respond well to CBT.
For what it's worth, I think it's unlikely you do have BPD, because that is usually diagnosed in a hospital setting during a manic phase.
I wish you all the best with your CBT journey, Steff. The key is that trust is established, but when it works, it's almost like magic.