You seriously won't have any problem. It's not a "general" anesthetic. Just some IV sedation. You actually are able to answer questions they may ask you as you really "aren't asleep". Part of the drug is that it gives you amnesia of the event, too, so you won't remember a thing, but you really aren't completely under. You just won't be able to feel any pain and you will have no memory of the event.
Do try to relax. I have had both IV sedation and nitrous oxide for tooth removal and it was fine. Just be sure to start with an ice pack as soon as you get home afterwards. To minimize swelling, sleep sitting up slightly. It usually is its worse around day three.
Have soft foods on hand so you can eat easily.
And, do try to relax, I PROMISE that it will all be OK.
Hope this helps.
Best to you,