I've had a left TKR, and a right THR, and my right shoulder worked on, and my right knee is next. I have 'OA' rather badly, at one point was seeing my heart DR rather often (now bout 10-12 months), and am on many different meds including both aspirin and Celebrex.
I have been taking NSAIDs for some 30 odd years (bloodwork every six months), and once I was put on blood-thinners, I had to switch to Celebrex. Personally, I have never had any stomach issues with any of the meds I take. As with any prescription NSAID, your DR will want to do regular bloodwork to monitor kidney and other functions.
That's my only point. Yes, at one point you were prescribed Celebrex, but your DR will need to know that you are now taking it regularly, as your med list may be different now than when it was prescribed for you, or your condition may be different. In my case, it could be a simple call to my DR's office, letting them know I've restarted it.
As for effectiveness, personally I've used different NSAIDs that worked better for me, but at this point, I have no other choice, and it's better than nothing. The reason they have so many NSAIDs available is that what works great for me, may not work great for you. I do agree, that rather than dealing with joint issues that can be painful, a NSAID is the step to take. Just be aware that by not having an Ortho check you out, you are risking possible new or more damage, if you actually tore something...