There's no requirement by the TSA that states you must have prescription medication in prescription bottles when flying.
But states have their own laws in which you must comply with in regards to medication and prescription medication and most state laws say that you must have the prescription medication in the original prescription bottles when flying or traveling.
Having the prescription medication at home in different containers is okay but when you have the prescription medication when you're traveling either by car, plane, bus or train etc then the prescription medication must be in properly labeled prescription bottles in your name if it's your medicine.