They have minifridges. My wife also has medication that must be refridgerated, and we cruised on the Radiance this past Feb.
Freedom Of The Seas -07
Radiance Of The Seas-07
Adventure Of The Seas-05
Navigator Of The Seas-04
Soverign Of The Seas-02
Big Red Boat-93
We requested in advance a refrigerator for my daughters insulin. Thought we were all set until we got on board and there were none available. (I had waited a couple of hours thinking that they would bring it). My advice is to make the request in writing in advance and to go to the pursers desk immediately upon arrival to confirm. We had to use a Mickey Mouse setup for the week.
We had her insulin in a small cooler on top of a bucket of ice in the room "chiller". Insulin can be stored at room temp for a month however the long acting insulin that we bring in case of pump failure also has a shelf life of 30 days therefore we have to throw it out upon our return.
Bottom line, send in the letter then go to guest relations immediately.
I am sure though that you could store it with the doctor though that may restrict your access to it.