A Prescription medication in a container with the Prescription attached to it (like a bottle with an Rx label) is considered valid as long as it isn't more than one year old. If it's a valid label listing the rx number, the doctor, the pharmacy, and it has your name on it and you have acceptable identification, that's good enough to prove it's yours.
If you have a paper prescription with you, you have a good chance of getting it filled, if you need to for any reason. I say a 'good chance' because I'm not sure what the laws are outside of this country and what pharmacies are like. I don't know if a Doctor licensed in the U.S. that writes an Rx for his patient would be a legal Rx in Mexico, for instance. If I needed to get an Rx filled while on a cruise, I'd start with the ship's Doctor.
If I were bringing a vital medication with me and I needed a reliable refrigeration method, I would ask my TA to get the Medical Needs form from
DCL and then fax it back to them. It would allow them to make provisions for storing your medication reliably and to be prepared for it. I use the form to notify them that I'm bringing medical equipment onboard as a treatment for my Obstructive Sleep Apnea and that I'll have to plug it into an electrical outlet.
hope that helps
edited : I know I read a document about taking medical equipment and prescriptions on airlines and cruise ships and the fact that you had the equipment and the medicine in original containers with a valid Rx was enough, but I can't find it now. I'll keep searching for it.