I think you should speak with your child's doctor about the egg allergy. Does your child have a documented allergic reaction or hypersensitivity to egg or egg products? If so, he may not qualify for the vaccine or at least should be evaluated by an allergist before giving it to him. Either way, if someone in the family is at risk for getting the flu, I always recommend that the entire family be vaccinated if possible, so that the exposure in that household is kept to a minimum.
When a child has asthma and an egg allergy, the flu shot may not be advisable. Consult with your child's doctor.
My son has asthma and is allergic to eggs. Can he still get a flu shot?
Each year's flu vaccine contains the three virus strains most likely to be around in the United States during the winter. Because the process of making the vaccine involves eggs, the risk of a reaction, if you are truly allergic to eggs, is possible. You should be aware that the vaccine itself is non-infectious (it can not cause influenza) and rarely causes systemic or febrile reactions. The most frequent side effect of the vaccination is soreness at the vaccination site that lasts for a couple of days. Most of the reactions are mild and rarely interfere with being able to do usual activities each day. The allergic reactions are felt to be caused by small amounts of egg protein remaining after the vaccine is made. Even though it is a very small amount, it can still cause immediate hypersensitivity.