It's never done that to me, for what it's worth. Because I had an ulcer at a young age I've been limited to taking acetominophen for OTC pain, and because antidepressants give me headaches I've had to use them. The big problem with acetominophen is it's highly liver toxic, so don't take it often or very much at a time. Also, I stopped taking the brand name Tylenol. It worked better than the generic, but they've been busted I think 3 times in the last few years for tainted products and taken off the shelves, so I've just given up on Tylenol brand.
Really anything can cause an increase in anxiety, although I've honestly never heard of Tylenol being a cause, nor have I experienced it, either personally or while working as a nurse.
While I'm sure it has happened, I would bet that there are things that are much more obvious, trigger wise.