The reason antiinflammatories are usually avoided in anticoagulated patients is that many of the NSAIDs can cause stomach bleeding.
Aspirin, and to a lesser extent some of the other NSAIDs, will also have an anticoagulative effect. However, that effect works in a different way than warfarin (Coumadin), and it won't show up in your INR readings, so you can't monitor it.
In some people, stomach bleeding doesn't seem to happen, or it's insignificant. In others, it can lead to a troublesome or even dangerous internal bleed. All indications seem to be that for mild and occasional use, most people fit in somewhere in the first group. The problem is that you don't know which group you will fit into.
In discussions on this board, naproxen sodium (Aleve) has often been touted as a less dangerous NSAID option for stomach bleeding. You can look up previous threads on this topic, where Al Lodwick has weighed in.
Acetaminophen (Tylenol) is not an NSAID, and doesn't have these issues. I don't know enough about HEAD ON, so I can't comment on that one. It doesn't go through the stomach, but again, I have no information on its action. A quick look at websites selling it does not show any warnings about not using with anticoagulant prescriptions. Just about everything else in pain relievers over the counter is an NSAID.
In any event, be sure your doctor is aware of what you're taking in terms of NSAIDs, don't take more than directed or prescription strengths of them, monitor for dark stool (not foolproof, but at least something), and don't take them continuously or frequently.
Best wishes,
