Yes, you are permitted to carry your own food on a plane if you don’t want to take any food from the airport. If you are healthiness conscious, then you can also bring your healthy food in your carry-on baggage. There are some food or things that airlines don’t allow you to carry on your checked luggage, like liquid or gel-like food products in your carry-on baggage.
There is some food allowed; if you need to carry all liquid, then for that, take that in packages of 3.4 oz, and these packages are all fit in one clear quart-sized plastic bag. Whatever you carry in your luggage, you need to give it for the security check-in, and then you purchase or eat the liquid foods or take it on the plane.