I have 2 herniated disc. It sucked for about 3 months. Walking definitely helps though. I think inflammation is a necessary part of the healing process and you should not prevent it using NSAID unless it's keeping you from sleeping. I went the home physical therapy route. Rather not get surgery for this type of thing. I'm only 26!
Inflammation is never good.
Some disc injuries require surgery, some you can get by without.
Usually prior to surgery, there is a multiple step path where NSAIDS, Steroids, PT and injections are possibly tried. If relief is not happening within 6 weeks, usually surgery is the only option.
There are micro-surgeries for many of these injuries now that really cut down on the recovery time. Basically they go in and cut the bulging part out a bit to free up room so the nerve(s) are not compressed.
I am not a doctor though, with this being in the coccyx they may just remove the disc and fuse the two bones together.