There are also other choices besides Psychologist and MSW. My therapist has a M.A. in Psychology and is a Licensed Mental Health Counselor (or something like that). I believe the theoretical orientation is important, whether you connect with them, and their areas of expertise. One of my T's major areas of expertise is Trauma. He is level 2 certified in EMDR and has been using other techniques as well with trauma clients for years. Since you mention DID, I would make sure the T had experience with this. (I have heard some Ts are not receptive to this diagnosis or don't know what to do with it.)

Good luck.