There's not much chance of something traumatic happening with the anesthesia, almost no chance at all. However, because of your great fear, you may want to reconsider having it, especially since you're only having two teeth pulled. I had 2 wisdom teeth removed a few months ago, and didn't get the anesthesia. It took my dentist all of 15min. to get my teeth out (one was partially impacted), I had none of the grogginess of the anesthesia afterward, and it just really wasn't bad at all. Plus it was WAY less expensive. If you were going to have all four wisdom teeth pulled I would definitely suggest the sedation, but for two teeth in the same area? For myself, I didn't think it was necessary.