Do I have trichotillomania?

Yes dear it is. There is good therapy now to treat it. I would see a psychiatrist for medication and Cognitive Behavior Therapy. For you, the medication will help with your depression, anxiety and compulsion. The therapy will help you break the habit slowly, and help you deal with past and present stressors in healthy ways. You can do this dear ! Please take care ! BIG HUG ! Chip