How To Overcome The Irrational Fear of Doctors and Dentists, Or Any Other?

Something I am struggling with is 'fear', and have been all my life. Fear of doctors. Fear of dentists. Fear of flying.
I probably could come up with a few more fears, more minor ones, but those three are my biggest.

This is interesting, considering that many of my friends would describe me as fearless. I left my home country before I was 20 years old, all by myself, and studied, lived and worked in various countries. I quite happily take solo vacations, hike solo and am generally not a worrier or easily scared. In fact, I thrive on challenges!

However, when it comes to a number of things, I have an intense irrational and somewhat debilitating fear. The worst and most dangerous of my fears is that of dentists and doctors. I don't know how many of you can relate, but I don't go to the dentist for years, and same with the doctor. I skip life saving prevention exams...heck, I have to be half-dead before I actually search any medical help, and even then only when friends and/or family practically drag me to a doctors office.

I know there has to be a reason for this but all I can think of was one visit to the dentist, as a child, where he told me to say 'aah' when it hurt and he said he would then 'immediately stop'. Drilling without anesthetic. He hit a nerve. I said 'aah' and he carried on. 'Just a little more'. It was so excruciating that my reflexes had me jump out of the chair and knock the drill out of the dentist's hand. He had not stopped although we 'agreed' he would, so I guess my trust for dentists was therefore broken irrevocably. However, I have been to the dentist many times since and although my visits are never enjoyable, I am usually lucky to have caring professionals. Still, I am petrified when I only think of going to a dentist.
Why the fear of the general doctor? No idea. It seems more and more irrational whichever way I look at it.

Now, I have to pass a medical for my green-card. Just thinking about it is making me sweat. Literally. There I am, googling all kinds of pages on how to help with irrational fears. I am deep breathing, or trying to, until trying to relax with deep breathing seamlessly leads to hyperventilating. What the heck? It seems like the more I concentrate on getting over the fear, the more it bites. A little like 'what you focus on grows'.

Yet finally I made the phone call to the doctors' office for an appointment. Just came off the phone before starting to write this. I feel ashamed to admit it took me days to even call them. For days I was procrastinating. Now I already know, the appointment being almost a week away, that I will feel sick just getting there, and my focus will be on just getting it over with without: fainting, hyperventilating, full blown panic attack and nausea.
It seems so silly and I can't even talk to my friends about this because I feel ashamed. ..yes, ashamed. Why can I not just 'get over myself' like everybody else?

I will let you know how the medical went....wish me luck!

Do you have fears? How much do they impact your life? Perhaps you have any tips and hints on how to control them?