I have had surgery, as for what type I'd rather not go into. But I was put to sleep with an intravenous anesthetic and it was a strange feeling. Not bad, just strange. When the anesthetist first administered it, I felt nothing, but then my arm (where the needle was) began to feel cold and then suddenly I found it hard to control my body, but I felt happy which was nice
After that I woke up after everything went swimmingly, but that's when it feels the worst, you feel so groggy and I thought I was gonna faint or throw up whenever I got up. That faded after a few hours though, so it was all fine.
As for being scared about a burst appendix, the surgery is incredibly low risk and there is little trauma. My girlfriend's father recently had to have his taken out after it burst and he was on more morphine before the surgery than after! It's keyhole surgery so he only has 3 tiny little marks on his abdomen to show for it.