Yes, you can. Some flu vaccines are made using eggs. As a result, the vaccines have tiny amounts of egg proteins in them. However, this doesn't necessarily mean that if you're allergic to eggs you can't get a flu shot.
There are two flu vaccines that don't contain egg proteins and are approved for use in adults age 18 and older. And even flu vaccines that do have egg proteins can be given safely to most people with egg allergy.
If you've had a reaction to eggs in the past, talk to your doctor before getting a flu vaccination. Your doctor may choose to give you the vaccine made without eggs or send you to a physician who specializes in allergies.
A skin test may be needed to see if you're truly allergic to eggs. A nurse or doctor will scratch a tiny amount of egg protein on your skin and watch to see if your skin reacts to it.
If the skin test is positive, you'll still probably be able to get the flu vaccine. Your doctor may want you to wait 30 minutes before leaving, in case you have a reaction.