An egg allergy in most people is usually due to the egg white protein and not the yolk protein. Like other foods that cause allergic reactions, a skin rash or more serious health effects can occur with this food allergen.
Many people outgrow an allergy to eggs at an early age. By the age of three to five years old, the sensitivity to eggs often disappears. However, this is not always the case. A severe allergic reaction to eggs can last for the lifetime of the individual. Allergy testing is required in order to establish that the individual no longer has an allergy to eggs.
It is often mentioned, that people with this type of food allergy can eat cooked eggs and not suffer a skin rash or other allergic symptoms. However, this is not necessarily true. Cooking does alter the protein of the raw egg, but this may not be sufficient to prevent an allergic reaction.
Another non-food related problem for those who are allergic to eggs is vaccines. For example, the flu vaccine is grown on the embryos of eggs. Therefore, there is a high probability that the vaccine contains egg protein and can cause a skin rash or other more serious allergic symptoms in allergic individuals. There is also concern about the Measles Mumps and Rubella vaccine (MMR) for people with a sensitivity to eggs. However, many years of use of the vaccine have shown it to be safe for egg allergic people. Nonetheless, if you have an allergy to eggs and are getting the above-mentioned vaccinations, it is best to consult with a physician prior to getting the vaccine.
Finally, like any food, eggs in food products are often listed under different names (source: Canada Food Inspection Agency). Be careful when reading ingredients and always double check the ingredients you do not recognize.