Then skip the flu shot. You (we all) need vitamin D about 5-10K IU per day in the colder months. That's the only vitamin which food will not give you, and the Sun produces. It's an immunity booster.
In winter, there is much less sun (so much less vitamin D is available for us) hence why our immune systems are compromised. Also, we are more often in closed quarters with too many people.
I haven't had a flu shot in over ten years. And also I have been taking vit D for about that time. And yes, no FLU in over ten years.
I suggest that you do research and not take my word for it, as I am not a doctor. And yes doctors and big pharma want us to take all sorts of shots and drugs, that's how they stay in business.