I would recommend always putting medications in your carry on as you never know what might happen to your bags.
You might be asked to check it, even if you had planned on carrying on, or it might go missing for a few days, leaving you without important medicine. It might throw a wrench in your plans, making you skip out on planned activities when you arrive.
Even if you do carry on your medications, something might happen while you’re traveling. It’s also smart to bring the written prescription with dosage from your doctor if you’ll be traveling for a while or if you need it immediately.
While I’ve never had any trouble with airport security questioning my pill containers, I have had trouble with medicated lotion whose label had worn off.
Since then, I’ve learned to put a clear piece of packing tape over it so that, if nothing else, you can see my name on the bottle. A clear bag with your pill bottles should do the trick.
Remember that if your medication is a liquid, you don’t have to worry about the TSA liquid rules as long as it’s prescribed. Just be sure to mention it to the security officer so they don’t think you’re trying to sneak larger liquids on board.