Hubris, thanks for the links. That "common faint" seems the closest (the symptoms seem similar), but the cause isn't an "emotionally traumitizing event". The cause isn't even something that bothers me, it's just stuff that evokes a physical reaction for some reason.
That's why they define a phobia as an 'an irrational and compelling fear or aversion'. Many times a person cannot explain what is so terrifying, traumatizing, or 'icky' about the thing to which they have a phobic fear or aversion. They just see it, or think about it, and a compelling reaction is produced involuntarily.
You're not alone, some three or four percent of the population has an involuntary and compelling aversion to the sight of blood. The psychotherapy is something worth looking into.
Basically you start by finding something that produces a minor reaction such as anxiety or feelings of impending doom, but will not trigger the full blown fainting reaction. Maybe just a picture of a needle by itself, not being stuck into someone. Or like you already said, just talking about cutting can get your heart rate up.
You then use reasoning and conditioning exercises to gradually increase your tolerance and comfort level with that minor thing. When you make progress, you move on to something a little more stressful. This almost has to be done in concert with a professional, phobias are rarely ever managed by attempting to treat yourself. Its almost unheard of, really, and can result in an even worse phobia than you had to begin with.
This is not going to happen overnight. It takes a long time and you have to be willing to expose yourself repeatedly to uncomfortable situations that are not very fun, as you already know. But the chances are good you can mitigate this reaction to something more manageable. Will you ever be 'comfortable' with being stuck with a needle? Probably not.