Almost everyone can get a flu shot: the CDC's no list is children under 6 months and people with a severe allergy to a vaccine ingredient.
Egg allergy alone no longer rules anyone out; the CDC says egg-allergic people may receive any otherwise-appropriate flu vaccine. Mild illness is not a reason to delay, and a past episode of Guillain-Barre syndrome within 6 weeks of a flu shot is a talk-to-your-doctor case, not an automatic no. If you truly cannot be vaccinated, the people around you getting theirs becomes your protection.
What to do
Common questions
Who should not get the flu shot?
The do-not list is short. Per the CDC, people who should not get a flu shot are: children younger than 6 months, who are too young for it, and people with severe, life-threatening allergies to any ingredient in a flu vaccine, other than egg proteins. Two common myths need correcting. First, egg allergy: the CDC says people with egg allergy may get any flu vaccine, egg-based or not, that is otherwise appropriate for their age and health, so egg allergy by itself is not a reason to skip. Second, being sick: a mild cold is not a reason to delay, though a moderate or severe illness usually means waiting until you recover, which your vaccinator will confirm. There is also a talk-to-your-doctor-first middle ground: people who have had Guillain-Barre syndrome within 6 weeks of a previous flu vaccine, and people with certain allergy histories, should discuss the choice with a clinician rather than self-deciding. And if you cannot get the shot, you are exactly the person who benefits when everyone around you does: herd protection and prompt antivirals if you are exposed matter more for you.