Flexeril is a muscle relaxer, not an anti-inflamatory, so it doesn't really do anything for arthritis, per se, it may just help the muscles that work around your joint relax, it's a muscle relaxer.
Almost any NSAID you take for inflammation is going to cause stomach upset. So far, I've found Celebrex to upset my stomach the least. If you have one particular joint that is flaring up, you can get cortisone shots, which in a couple of days does wonders for the joint. I've had the Synvisc injections in my knees a few times (it's like a lubricant that helps keep the bones from rubbing together), but after the first couple of times, it didn't work (for me) either. If you have more than one joint flare up at same time (let's say like you wake up and several joints are involved at one time, like your left knee, left shoulder, and wrists) you can get a steroid taper-packet....to me, this is like a miracle drug, after a few days I feel like superwoman! But when I say "Flare up", I mean these joints aren't normally affected all at once everyday, it's like your body is revolving on you all at once and your joints are red and swollen.
There may be times when you really need a narcotic pain reliever. Before my knee surgery, I was taking a Percocet every night, just to be able to sleep through the knee pain.
Those with RA are a complete different complex issue, that's when they bring out the "heavy guns" of medications. I feel really bad for those with RA that can't keep it under control.