One way to quickly tell if your narcotics are tylenol based and not NSAID based is by their name. For example, Lorcet and Percocet have "cet" in their names, which means "acetaminophen", or tylenol.

Vicodin also has tylenol, Vicoprofen has ibuprofen. Percodan has aspirin, another "bleeder", so don't use that. Just make sure, you can't feel it when your platelets are low. It just shows in bloodwork. I was such a case (with low platelets and no major bleeding) that they were bringing in all the docs around to "show me off".