I used to be exactly the same. When I was 11, I went into hospial to have my appendix removed, and (I have bad veins) it took 19 attempts to get a drip into me! Needless to say, I came out of it a little traumatised!
But, I'm cured now! Even gave blood to the Transfusion Service recently. About three years later, I was working in a hotel bar, and every week we had a stage hypnotist come in. One night after his show we got talking, and he told me he done therapy work too, and I told him about my phobia.
He went away and researched it, and the next week, before his show, took me up to an empty room in the hotel. He laid me down on the bed, and just talked calmly to me for about fifteen minute. I didn't pass out or anything, and I remember everything he said. But it worked! Crazy as it may seem, I swear by it.