Tylenol is a heck of a pain killer and can be taken on an empty stomach. Most hard core pain killers are some version of Tylenol + some opioid such as codeine. Heck codeine itself is mild on the stomach but it can still cause mild side effects which is why it is recommended (but not needed) to be taken with food.
Ask your doctor for something less likely to upset your stomach. If it still does, have a medicinal glass of milk.