In all likelihood your colitis is indeed gone, but it's not guaranteed. Some people do get non-intestinal symptoms of colitis, some develop colitis in the small cuff of rectum left in during the surgery ("cuffitis"), and some develop Crohn's disease.
NSAIDs have some extra problems for people with J-pouches. At a minimum they increase the risk of pouchitis. Nevertheless, some people successfully use them for years, though.