I’ve actually had quite a few procedures done on my mouth, including 2 root canals, and I did it all with just a local anaesthetic and I can say that just getting teeth pulled is probably the easiest. I think that wisdom teeth have a much higher chance of requiring surgery though. Even so, you probably won’t even need any stitches. I think actually getting the shot is the worst part of the whole experience. It does actually hurt a bit for a few seconds, but beyond that, it’s really nothing. The actual pain of teeth and gum problems is usually 10x greater than anything you experience during or after a procedure.
It’s very likely that you will need to have more dental procedures done in the future, so if you really want to get over your fear, it might be a good idea to actually be awake for it so you can see that it’s really not that big of a deal (most of the time). Afterward, just follow their instructions… make sure you don’t do anything to dislodge the blood clot for about 24 hours and you should be fine. I’ve had numerous teeth pulled and I’ve never had a dry socket or any other complications.
Before my first procedure (which happened to be my wisdom teeth as well), I actually called the dentist and told him I was having anxiety issues and he gave me something to calm me down a little bit before my appointment, so that may be another option for ya. This is my first post here, btw. I hope it helps! Good luck.