Chiming in:
1. I'm not, if you'll pardon the expression, married to the idea that my children be my own offspring. I have a bit of an unconventional family, and it's taught me that there's much more to being a family than just genetics.
2. If you're looking at a real, long-term relationship, you SHOULD probably settle the question of whether it's important to the other person to have (or not have) kids, and details related to same -- if not right upfront, then at least early on. (If you're looking at something more casual, then it's important to be on the same page regarding birth control, abortion, etc.)
3. To the best of my knowledge, nobody here is qualified to dispense professional medical advice, and anything we offer up is conjecture.
That said, my conjecture is that simply choosing not to have kids may not be enough to cope with a phobia. Phobias are, by definition, irrational; even if you're physically incapable of bearing children, you may still find yourself afraid of the prospect. If there's a way to get over your fear of childbirth, it's probably worth your while to pursue it, even if you decide to pursue a long-term (or permanent) form of birth control.
Of course, you're also going to want to research WHAT form that would be. An IUD, for example, is a very effective method of birth control, but would most likely be a poor solution to your problem, as you have to go into simulated labor to get one inserted.
Bottom line, of course, is that you should keep talking to professionals instead of people on the Internet.
