Unless some TSA clown tries to exceed his/her authority, you should have no problem, just carry the pills with you. Solid pills are allowed. That is not to say that the TSA people actually obey their own rules.

As far as U.S. Customs goes, I wouldn't worry so long as you don't have anything scheduled (opiates, amphetamines, cocaine, etc., basically anthing that could be seen as "fun") and the qty of pills is not too much more than a 30 day supply (for a 30 day trip).

Carry as much documentation as you can anyways.

IANAL.