I'm sorry, but once again, I feel like your therapist is sending up red flags of her incompetence. I wonder if she has even looked at the diagnostic criteria, or if she is just talking out of her ***, as seems to be her MO.

Yes, you can have OSDD and have not very strong alters who don't lose time. Alternatively, UDD might fit you better. I'm not a clinician, so I can't diagnose you. However, it doesn't really seem like your therapist has the necessary knowledge to diagnose you, either. Knowing that, I hope you will try not to allow whatever diagnosis she goes with to overly distress you.