Is it possible for you to drink wine while taking an anti-inflamatory?

Depends on how much: if you are talking a glass or two, as long as you have no history of peptic ulcers, gastritis or heartburn, there is little likelihood that that amount of alcohol and an NSAID are going to cause problems. However, larger amounts of alcohol can increase the chance of gastritis and gastrointestinal bleeding, as well as reflux and heartburn.