To be honest, I would request the ice
Seriously, the fridges are NOT cold enuf for anything to be kept cold much less cool.
If you put a bottle of water in the one we had it would only be a tad cooler than never being cooled at all.
Not worth the risk with meds.
2005 Carnival Spirit to Alaska
2007 Carnival Conquest to Western Caribbean
2008 Royal Caribbean Explorer of the Seas to New England/Canada
2010 Royal Caribbean Explorer of the Seas to Southern Caribbean