somewhathorrified - I do understand your medic phobia. You have to drag me kicking and screaming to the doctor under normal circumstances. Hate it, hate it, hate it. All that talking about yourself (happy to do it on here, but in front of a real live doctor or nurse...).
But, I do think having a reasonable amount of knowledge about what your body is going to try and do, and some ideas about how you would like to deal with it will put you more in control and perhaps help you control your phobia?
It is true that your body is built for this, but your brain has not had to listen to your body as it tries to do this before. As you feel things you have never felt before, your logical brain may make you resist, but if you've read about what is supposed to be happening, then your logical brain can help you not to resist.
For example, I made the mistake of telling my inlaws when they called that they couldn't pop in for tea as I was in labour. 15 minutes later there they were on the doorstep insisting they should take me to hospital (I was still about 8 mins apart, midwife had just told me not to get excited, it could still all stop). I had read that stress can slow your labour down, so, much as I hated having my FIL timing my contractions and my MIL telling me it was okay to make a noise (I really didn't need to at that point), I concentrated on staying calm and not letting it stress me, so as not to slow it down. (it did slow slightly, grr, but not too much). I think if I hadn't read about that I would just have allowed myself to get all pissed off and tense and the labour could have stopped altogether.
Also, I had no urge to push whatsoever. So you body may not let you know everything you need to know.
But, that said, it is still very early to be thinking much about this stuff!