I had 4 wisdom teeth removed last December. I was extremely anxious before the operation, too. They gave me general anesthesia through an IV, so I don't know what local with sedative would be like. The operation itself went fine, but I had soreness and swelling in my mouth for the next week. Luckily, the doctors gave me painkillers to help with the pain. The total recovery took about 2 weeks, but your recovery should be shorter because it's just two teeth, not four.