Yes unlabeled pills can be brought onto the plane but it's recommended you do carry the prescription with you proving that the pills are your own pills.
I've brought pills onto the plane in those medication containers that states the day I take the medication and it never has been a problem.
I've never been asked for the prescription but I have it with me just in case because you never know if they will ask or not.
The pills will just go through airport screening and they will be allowed onto the plane.
You can also bring liquid medication onto the plane without a problem.