one of my friends has this problem as well. she goes to her dr, tells him the problem, and he prescribes her a single dose of a tranquilizer to take 30 min before her dentist appt, or eye appt. or flight. or booster shot. or really any medical procedure other than a simple appt.
There are dentists who specialize in sedation dentistry. When I went in for oral surgery for my gums, I took a little pill on the way in the door, and don't remember one more thing about the entire event. (Of course, my husband was there to drive me home -- don't try this without a ride home.)