Can a flu shot give you the flu?
No, a flu shot cannot cause flu illness. Flu vaccines given with a needle are currently made in two ways: the vaccine is made either with a) flu vaccine viruses that have been ‘inactivated’ and are therefore not infectious, or b) with no flu vaccine viruses at all (which is the case for recombinant influenza vaccine). The most common side effects from the influenza shot are soreness, redness, tenderness or swelling where the shot was given. Low-grade fever, headache and muscle aches also may occur.
In randomized, blinded studies, where some people get inactivated flu shots and others get salt-water shots, the only differences in symptoms was increased soreness in the arm and redness at the injection site among people who got the flu shot. There were no differences in terms of body aches, fever, cough, runny nose or sore throat.
See more here: https://www.cdc.gov/flu/about/qa/misconceptions.htm