have been to USA twice with our allergic son, eggs/nuts/beans/yeast extract/kiwi allergy etc! (not milk though)
we brought own food for son on plane, he did have to sip his liquid antihistamine, so you might need to do same for other food liquids.
get a doctors letter , from GP or allergist, describing medical condition, medical issues and need to take own food.
get extra medical insurance just in case. it cost us about £150 just for our son.
you might want to wipe down the seat and tray, but wipes alone don't do much to remove visable food traces.
I think you can buy seat covers online I think its an American company that some people use for children with allergies. other than that you could spread a blanket down. my son was 10 when we went so much older than your child.
medication, get extra autoinjectors if can from doctors for the flight.
split in to 3 separate packs : 1 for me, 1 for son to take on flight and one in suitcase should one go missing. we had about 5-6 on flight
As for food, large supermarkets are best, USA like us has plenty of allergic people and do have free from sections.
Even if you are staying in a hotel, buying food and eating it picnic style is possible and eases the stress of finding 3 safe meals a day iyswim
on our first trip to USA we even took an internal flight with son, and had not problem we stuck to taking our own food and we were all ok. no problems at all.
travel is totally possible with food allergies, and with lots of preplanning is worth doing to raise your confidence and eventually your child as they grow older.
please ask any more questions and I will do my best to help.