Both of my kids had impacted wisdom tooth and they were hard to be removed. D1 had hers removed 2 days prior o Thanksgiving and was able to eat some turkey, but D2 was not able to eat until 3-4 days later. We used the same surgeon. He was very experienced, so I think he wasn’t as rough on their jaws. We also followed the recovery instruction to a T. They didn’t go out or had friends over for few days, slept sitting up, gargled with salt water and put cold compact on and off. My kids’ face started to look better after 3 days. The older one didn’t have much of swelling, but the younger one did.
You don’t have to be at school until Sep 5 (move in day), maybe even later, that’s 11 days. You probably could even show up later if there is complication. I would have it done, keep your current flight, and change it if necessary.