I would definitely explain it to your psychiatrist, but try not to jump to conclusions about it being DID. Explain what you told us and ask "what is this?"

In my opinion, which probably doesn't matter much, it sounds like you're "splitting". Which is common in BPD. It doesn't mean you have two different personalities. Maybe you could do some research on it and see if it fits? Also look up projective identification in bpd.

The thing I could find explaining splitting was "A person with BPD may see themselves as “good” one minute, but shift to seeing themselves as all “bad” or even evil the next."

"the "failure to integrate shame experience into the self leaves the shame experience split off and having to be managed by another psychological system. This is how the "false self" of BPD develops"