Yes and no... Depersonalization is/can be a part of DID. You shared that you didn't know what went on in the session, so you were dissociated fully at that time, imo. During DID there can be times where you are not in control, but are aware of what another is doing and saying. For some other parts/alters of you, you may not be aware at all. As you begin to heal, and if your system is merging for that healing, then ultimately you will be aware and somewhat in control of what you are doing and saying pretty much all the time.

I think it's great that you/your system felt safe enough to share with the T! Perhaps you were stressed out about the MD visit, and either you couldn't handle it with the T, or the other part of you needed to discuss it or something with the T. It's all good, and your T sounds like someone who is able to help you with this.

Part of DID "allows" for a personal experience. That may sound conflictive regarding such a non-personal type/feeling disorder. But everyone's experience with this disorder is different, and uniquely their own. There is no right or wrong. You have in your infinite wisdom, used this ability to dissociate to protect yourself in whatever way you needed to. That's marvelous. Don't fear it, as it's all good and ok. As you progress with your T you will find many scary times, and confusion will probably come with the "program" too...but stay the course and trust your T to guide you safely through.