I've taken a lot of prescription meds through security in carry on luggage and never had an issue. (At times I've been on 5 or more prescriptions at a time.) Sometimes I would put my prescriptions in a plastic bag and remove it before going through the scanners (similar to what you do with liquids in carry ons) but this is unnecessary. I never was asked to explain what my medications were for.
However, in my case, none of the meds were controlled. I would think it would be a good idea to only bring about as many pills as you need for the duration of the trip. If you just got a refill and are travelling with a month's supply when your trip is only 3 days (I'm just making up numbers here), then that may draw more attention then if you bring just a 4 day supply (enough for your trip plus 1 emergency extra.)
If you are really worried, you should call TSA and get advice for your situation. I just googled "TSA hotline" and found a page about how travelers with medical needs can get advice. At the bottom of the website, it lists contact information that anyone (not just those with medical needs) can use to ask questions to TSA.
I have traveled in the US and to Mexico, as well as the Caribbean Islands and have never had any problems at all. I know many people, like myself who have kidney stones, carry "what if" and routine medications with them. I always keep them in their original container with the prescription. I like the link above to check with the TSA to be certain. Sometimes, I'll split my meds up (carry on and some in my suitcase) just to be certain I have them in case something unforeseen occurs.Your pharmacist can generate a duplicate label and generally will give you an added empty container.
Have a great trip!
To be hired by the TSA you have to pass a test and score below thirty out of five hundred possible points. They are irrational, and any protest will likely get you arrested. In thre past I ferried a multi-engine aircraft from New Orleans to the East Coast and got handcuffed by them walking from the plane to the terminal. On another ferry flight, I was dressed lightly (I came from Floriida and ended up in Boston in a snowstorm. They TSA had the door to the terminal locked and refused to let me in because I "didn't have proper ID". I said "I am out here with the airplanes, you idiot! You are inside in the terminal! Does it look like I am going to hyjack the terminal!"