I don't suffer from extreme touch anxiety. I don't like people to touch me, but it's only truly bothersome or annoying to me when I'm in public and the touch is undetected before it occurs. To me a doctor's exam is just a bunch of annoying poking and prodding. It doesn't cause the same stress for me.
My wife has similar challenges to what you describe, and therefore uses female doctors exclusively. Perhaps there are even some who specialize in post-traumatic-stress exams?
Even though your aversion isn't PTSD-related, you may benefit from the same techniques employed by those types of doctors. If the challenges do happen to be rooted in a traumatic event, I'd recommend instead that you address the underlying cause rather than work-around the symptom.