For the most part, yes!
According to the American Academy of Pediatrics, children with mild egg allergies, such as the development of a rash or hives, but without severe symptoms such as vomiting, shortness of breath, or shock, can safely receive the influenza vaccine. For these children, the shot is the approved method of immunization. For children with a severe egg allergy, the influenza vaccine should not be given until consultation with an expert in food allergies, such as a pediatric allergist. Talk with your pediatrician to make the safest decision possible for your child.