As long as we're talking about food in carryons...

When we take our upcoming vacation to our timeshares in Orlando and Puerto Rico, I'd like to take a rolling cooler with me with some food in it. We are on a restrictive diet and I don't want to have to bother to shop for a lot of this stuff during vacation.

Could someone please confirm that you can take additional liquids with a doctor's note about being medically necessary (since our diet is)?

I want to pack frozen containers of Egg Beaters (keeps stuff cool and much more expensive to buy individually at some remote grocery store than by the case at Costco), possibly some frozen raw meat (like chicken breasts & shrimp), some prepared frozen foods, like homemade soups. As long as I'm packing in that stuff, I might take along some additional beverages, produce, etc. Also, can I back frozen gel packs to maintain the chill?

I wouldn't want to check the cooler because of the warmer temperatures in cargo and possible delays or misdirected baggage causing spoilage.

I'm pretty sure the cooler could fit in the upper compartment, it's not a huge Igloo cooler, it is soft sided, has wheels and is about the size of a carry on suitcase, only more cube shaped. The largest dimensions are 15" x 15" (it's sloped shorter in the front).

I appreciate your guidance.