Back in 1980, I had all four wisdom teeth removed at age 18, all impacted under bone. I was prescribed pain medication, but didn't need it, b/c I hardly had any pain at all, expect when chewing. The day after my surgery, I was out on the driveway hitting tennis balls with my father. I don't remember having puffy cheeks.
As for general anasthesia, I was on the operating table, and it seemed like the next second, I was in the recovery room. No sense of passage of time like when you wake up from sleeping. Felt nauseous when I woke up, threw up, and then was fine.
I was fine, and that was 27 years ago, when medical technology was less advanced. I suggest you relax and try not to worry about it. You'll be fine too. No need to cause yourself any unnecessary stress and worry.