I was checking US Customs the other day for similar reasons (7yr old but with food issues) - and my plan is to bring some with me (dry foods), buy sambos etc and fill water bottles after security (DH brings his Bobble bottle all the time and no hassle once it's empty at security - but he refills in the lounge with Evian, we'll be at water fountain on tap).
But it also looks like it's not as bad as I feared for bringing things off the plane either (we have an internal flt afterwards). It looks like hard cheeses are ok, but not liquid cheeses (cottage cheese) or yoghurt. Fruit and veg are ok (except anything citrus) and dried fruits, muesli bars etc all fine. And I think I am ok to bring my Barry's teabags for my morning cuppa too.
NO MEAT - so eat your ham sambo on board or leave it behind. Or your pepperami or whatever.
Check the US Customs website yourself though to be sure of the things you are likely to want: US Customs
On arrival to the US, Any food, whatever it is, anything you can eat, needs to be declared on your customs form. Even if you think its allowed, DECLARE IT!! US customs do not have a sense of humour and will fine you heavily for undeclared items. Dogs patrol most baggage halls. Dont risk it. Read your forms and declare any food anf you will be fine.
I was also wondering about the protocol regarding food on an aeroplane, I will be flying to crete which is around 5 hours, I do not think there was the option to arrange some lunch on the plane, but rather than having to buy food at the airport due to dietary requirements (and expense) I was hoping to bring my own food, but it's been a while since i've flown and I can remember! Can I bring sandwiches and snacks, obviously no bottles of water through security, to bring on the plane?