Airport security, particularly in the US where many airports have international and domestic departures out of the same terminal, will not care about that. I regularly travel with OTC pills loose in a container and no documentation, and have had no issues.
Where you might encounter problems is on entering that foreign country. While they have never ever given me grief over my OTC medicines, I try to make sure to remember to buy stuff in original packaging to bring. But even then, as long as you are only bringing enough for your trip they probably won’t care. Prescription medicines should absolutely be in original containers, though.