YES, you CAN carry all the food (and drink!) you need through security -- but you would be wise to have physician's letter stating medical need and using the term "disability". The TSA advisories address this at their website -- in the passengers with disabilites sections. The "child under age 2" food rules won't apply, as the disability qualifies for special treatment.
And once you clear security, you make a bee line for kiosk that sells water/beverages to add to your carry on beverage supply, if needed. (Lots of people take empty water bottles through security and then fill them up at drinking fountains before boarding.)
You can also accept beverage in bottle/can from attendant and then wipe off, which might help some. (Use own cups that you bring on board?)