You have to tell the airline over the phone about your child's allergy and they will make preparations to not serve whatever your child is allergic to to the other passengers. Also, you can arrange to go on the plane first and clean the area for your child, with wipes. Wipe down everything they would touch, arm rest, food tray etc. And make sure you have all of your child's medicine on hand so that you can access it if you need to before you land. They can't stop other passengers from brining on their own food, but they'll make an announcement once everyone is in the plane to avoid consuming those products/food. But you have to tell them before boarding.

I pack my own snacks after letting the airline know about my allergy and clearing it through them.

If allergens are air born, place the mask over child's face. We are doing that every time flying.

Delta air was allergen helpful. Announcement before boarding. Other airlines not so!

Let the airline know beforehand! Remind stewards of their allergy as well, when boarding