Yes. Children can receive the flu shot and COVID-19 vaccine simultaneously. They can also receive any other necessary vaccines at the same time too. The physician will administer each vaccine in a different injection site, likely in the same arm, so it’s possible that your children will experience some soreness in the injection sites. If in need of relief, give your child ibuprofen or acetaminophen to help with the pain. You can also place a cold, wet washcloth over the tender area.