Naproxen taken on prescription might be okay in limited quantities and taken with food while also on a DOAC or similar anti-platelet. But there's still that risk of stomach bleeds. Tylenol would probably be safer, but I don't know that...a doctor would...or should.
I think the origin of the inflammation should be controlled and hopefully the inflammation will subside and become moot.
The instructions I've been given by two EPs is that NSAIDs are okay for short-term use -- less than a week. Otherwise, Tylenol or a prescription drug such as tramadol.