I think you could benefit from talking to a professional counsellor. They can help you avoid 'going to the emergency room' in your head. Your fear is premature, as you pointed out, and a little irrational. I say this in a gentle way. The chances of anything truly terrible happening (i.e. your death, or the death of the baby) are slim to none. It's like worrying about your plane falling out of the sky, when statistically speaking, it's not going to happen.
That said, what IS is about mothers wanting to tell everybody their childbirth horror stories? Especially new mothers. So many new mothers seem to enjoy terrifying everybody with stories of gore and panic. I think it must be a 'badge of honour' thing. Yes, absolutely, things can (and often do) go a little bit wrong. You could end up with a big perineal tear, or a caesarian section, or some other unexpected complication. (Maybe your baby will be born on the hospital's front steps, like an acquaintance of mine! Awesome and extremely funny story). But nothing will happen that can't be fixed. Bodies have a remarkable ability to heal.
When pregnant with my first child, I was absolutely (and irrationally) convinced that the baby wouldn't fit. I begged the obstetrician for a planned c-section. I was worried the baby would get stuck and get brain damage from lack of oxygen. He reassured me that everything would be fine. He was right. (And like you, I have an extensive background in biology. I know exactly what kinds of things can go wrong).
As for fear of pain? Natural childbirth is all well and good, if you go in for that sort of thing, but if you don't, ask for an epidural. They are magic. Don't let anyone convince you that you can't push when you're numb from waist down. I had two straightforward vaginal deliveries, both with an epidural, and it made the birthing experience fun rather than a fog of agony. Breathing techniques and meditation are mildly helpful, but nothing eliminates pain like anaesthetic injected right into your central nervous system. (Think of it this way: would you want to get a filling without Novocaine?)