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If you state which ship you are on you may get a respons.
My sister went on a cruise last year with RCI and she has to inject for MS. She found that they not only had a fridge but were also given a sharps bin for needle disposal. She was only on a 5 day cruise as part of a much longer multi centre US holiday and found the attitude and helpfulness of RCI with her medical requirements far surpassed anything she experienced in the hotel she has stayed in (including 5 star ones). So I'm sure you will have no problem. If in any doubt, contact them before you sai.
Not all RCI ships have Fridges in cabi.
If you make a request for a fridge then there will be one provided in your room. All you have to do is ask.