The abbreviation of Reactive Arthritis is (ReA) so it won't be confused with Rheumatoid Arthritis (RA). I only know this because a poor resident doctor reported to my staff rheumatologist that I had a "history of RA." The staff rheumatologist pounced and said that wasn't true. There was an awkward silence until I said I had reactive arthritis (ReA).
----------------------
ReA falls under the umbrella of a "family of disorders" known as Spondyloarthritis. There are several types of Spondyloarthritis but they all have similar characteristics. There isn't much research that is done specifically for the treatment of ReA. In part, this is because of its association with Dr. Reiter.

I think the general guidelines are to treat the offending infection first if the infection hasn't already resolved. NSAIDs come next and if that isn't enough, then methotrexate is added.
https://rheumatology.org/patients/spondyloarthritis
Collectively, chronic and recurring forms of spondyloarthritis are treated with TNF inhibitors. I always had a flare of uveitis that would accompany my reactive arthritis flares. My ophthalmologist used high dose Prednisone-- usually 60 mg to start followed by a fast taper. That kind of dose of Prednisone alleviates almost any kind of inflammation and pain.

After more than 30 flares of uveitis in 20 years, my ophthalmologist referred me to a "uveitis specialist" who said I should have been referred to her a long time ago. She recommended Humira, a TNF-inhibitor so as to prevent the flares from recurring so often.