I was given very specific instructions NOT to take any NSAIDs or really almost anything else other than what was prescribed. I did have a prescription for a a drug to reduce nausea, but ended up not needing it. (Previously I had experienced nausea on prescription pain meds.) No Advil, no hormones, no vitamin supplements.
Ice helps, and rest, and time. And sheesh, yeah, you have this kind of surgery, you're going to have some serious swelling. Forehead work is like a really bad black/puffy eye. Chin work — that's even worse, because there's more soft tissue. The part that was really surprising was the swelling inside my mouth. Like, my gums puffed up and my lips inside and out and my cheeks and it was all pulling on the sutures really hard until they came out (and it's still a little weird). And this is all normal, per my surgeon and other doctors and nurses I have seen since.
Just wait a week or two, and that all comes down. I'm at a little over two weeks and my chin is still tender and slightly swollen but everything else is fine, except a little weirdness where the sutures in my cheeks were.