Hi, I believe that it is OK to take tylenol, but not over a certain amount per week. You might check Al's website for specific information (click on links on the main VR page and then on Coumadin and then warfarin.com.). I know I have taken tylenol with codeine and hydrocodeine and have not had a problem with my INR from them.
You are not supposed to take ibuprofen or aspirin due to the risk of gastrointestinal bleeding.
I have back problems and I have taken Alieve, Tylenol, celebrex, and finally Hydrocone. I didn't see any major difference except with the hydrocone, my INR seemed to be hovering around the low end and I have yet to get it up near 3.0 seems like 2.1-2.2 is whaer it stays. I am slowly adding a little more to the dose but it takes forever.