Well, I'm also female, just a few years old than you, and I've been under the knife twice so far. The first time was to pin my broken hip after my horse threw me into a fence, and the second time was for gall bladder surgery. With both cases there wasn't a whole lot of time between the "here's what's wrong, you need surgery" diagnosis and the actual surgery, so I didn't have a lot of time to get scared over it - and with the gall bladder, I wanted the surgery done yesterday because I was sick of throwing up everything I ate!
I didn't think about the anesthesia beforehand, and it wasn't bad. I had an IV inserted, which is no big deal; if you've ever given blood it's much the same. I was told to count back from 100. I remember getting to about 96 each time, and then I was waking up in the recovery room.
For me post-op and recovery was worse; I have this aversion to taking pain meds even when I should. I'm the type who takes the minimum necessary just to get some sleep and take the edge off so I can function. Your family should be prepared to have you incapacitated for several days after you get home.