Yes, studies have found that it is safe and effective to get both your flu shot and a COVID-19 vaccine at the same time; because the two vaccines are for two different viruses, your body is still able to mount a proper immune response against both of them. If you typically experience side effects after the flu vaccine, or if you had side effects after an earlier dose of the COVID-19 vaccine, you may experience similar side effects after getting both at the same time.