Don't be frightened, I understand that Dentists and needles are frightening but this time they will place you under general anesthesia. They will put you to sleep and you won't feel a thing during the entire procedure. When you wake up, the procedure will be done and they will give you painkillers. Your recovery should even be faster since it will be done under general anesthesia.
If you're afraid that they will place you under general anesthesia, maybe you can have you mom or dad accompany you inside the surgery area. So you will see them before you go to sleep and ask if they can wait for you in the recovery room, so when you wake up, they will be the first person you will see.
I have been through wisdom teeth removal and they did local anesthesia only. I didn't feel anything during the procedure, just pressure while they were extracting the tooth. After, some painkillers were fine to keep any pain in check. I remember it being irritating that your jaw is swollen and you can't eat everything that you want. I don't remember it being painful, just REALLY irritating.