Two times I had severe inflammation and soreness that RICE (rest, ice, compression, elevation) didn't bring down. Those cases were scary: I was worried something very serious was wrong.
I hate using drugs, and almost never use them, but both of those times I took over-the-counter ibuprofen (yes, it's an NSAID) at the dose indicated on the box, and both times it worked perfectly within a day or two. Magic!
As far as I know, no skating organization will disqualify you for using ibuprofen, and it seems pretty common, though I suppose you could check.
If ibuprofen isn't enough, I would personally would see someone with a sports medicine specialty - either a Sports PT/ATC, or a physician who specialized in sports medicine. It' expensive, if your insurance won't pay, but bodies are difficult to replace, and what you say sounds scary.
Or do you live in a country where it is illegal to see medical personnel without red tape, even if you pay?