If you're allergic to eggs, it means your body misinterprets certain proteins found in eggs and overreacts whenever you eat them. There are allergenic proteins in egg yolks and in egg whites, and allergies to egg whites are actually more common than allergies to egg yolks. Whenever you eat an egg, your body registers those proteins as dangerous, even though they're not. The proteins set off your immune system and trigger an antibody called immunoglobulin E to be released. The antibody then signals a bunch of chemicals to fight off the protein. One of those chemicals is called histamine, and it's responsible for most of your unpleasant allergic symptoms.
Even if you're only allergic to egg whites and not to egg yolks -- or vice versa -- you still have to look out for foods that are made with eggs. While some people's immune systems can handle cooked eggs, many people with egg allergies still find cooked eggs, including egg whites, problematic.