Theoretically the FAA would like you to contact your AME any time you are taking a new medicine.
The reality is that most folks don't do this. The FAA does not publish a public list of allowed meds because the effects might vary between individuals, and the underlying illness might also be grounding.
There are however a variety of informal "approved med" lists which are probably pretty safe as far as common meds go. These folks publish one, and include some narrative: "http://www.aviationmedicine.com/"
Note that most "approved" meds require a non-flying trial period (usually 12-48 hours) if you have never taken the med before. This is to ensure you have no unusual side-effects.
There are some OTC cold meds which are no-go, do your OWN research...SKW just fired a CA who was given a cold med by an FA and then failed a whiz-quiz (she took the FA's word for it
). I did the research, bought some approved meds and labeled them as good-to-fly....that way I won't grab the wrong pill by mistake.
Also if you look on the FAA medical form it only asks if you are currently taking anything...it does not (like the military) ask if you have taken any meds since your last medical. The way I see it, if you are not on meds the day of your medical and did not see a doctor about a past illness you don't have to mention it.