The Spondylitis Association of America has good information about Reactive Arthritis [ReA].
"Disease Course / Prognosis
ReA usually develops 2-4 weeks after the infection. A tendency exists for more severe and long-term disease in patients who do test positive for HLA-B27 as well as those who have a family history of the disease.
Reactive Arthritis typically follows a limited course, where symptoms subsiding in 3-12 months. However, the condition has a tendency to recur. about 15-20% of people with ReA develop a chronic, and sometimes severe, arthritis or spondylitis."
If you are lucky and things subside on their own and you have no recurrence of symptoms, you might get away without taking medications. However, there are those with this type of arthritis that have severe, long-term problems that cannot function without medications.