I actually had the same issue with my wisdom teeth as far as the nerve goes. I got all 4 of mine pulled and yeaa they weren't completely out of the gum yet, so they had to cut threw my gum's to get to them. I was awake for the whole thing. . .I think everyone usually is though, anyway.
They gave me like 4 shots of Novocaine and went to work. I heard everything, when they were going threw my gum's I don't think they were cutting, it smelt more like burning threw them lol, that didn't hurt at all. The only time it hurt was when they were actually pulling, I felt it more inside of my gum's, and that wasn't that bad pain level of like a 4 out of 10.
After the Novocaine started wearing off later that day is when they started bothering me, I looked like a chipmunk because I had gauze in my mouth to soak up all the blood. When I opened my mouth to wide to laugh or something I would accidentally pull the stitches they put in...which is something to watch out for. In the end I did end up pulling the stitches out on accident and I had wash my mouth out to get food out of one of the holes lol.
You'll be fine, it's not as bad as people make it out to be. . .Good luck.