I am allergic to sulfa antibiotics and found this out on the way back home from the Cleveland Clinic last year. I ended up going to an emergency room where they gave me benadryl. I was mad because I had a bottle of benadryl in the trunk of my car. If I had known that was all they were going to do I would have taken it and kept driving. But, seriously an allergic reaction can be very serious which is the reason I did call 911 on my cell phone and went by ambulance from the state highway patrol station to the hospital.
On the second part of your question, I have taken celebrex before without any complications so I would try it out. There are warning though that it can possibly cause heart problems and stomach bleeding do to it being an anti-inflammatory. I would definitely consult your doctor and see what he/she thinks.