Unless your fingers were swelling like this before you started taking this medication, I think you should stop taking the medication and call your doctor. Sulfasalazine should reduce swelling, not cause it. It is possible that you are having a reaction to the drug.
I am 31 and just diagnosed with Spondyloarthropathy as well. My main symptom is that my right hand and fingers swell. My joints ache and my elbow and upper arm get a little swollen. I am trying to do a little research on this and can't really find much about swelling in the hands. Is this common with Spondyloarthropathy?