Is it true that getting the flu shot each year can actually lower your immunity in the long run?

I've been getting the yearly flu shot every year since I was 12, when I found out I had more white blood cells than red, so it is easier for me to catch stuff from other people. I feel fine and am now in my 20s. I've never heard of that, and the fact that it's the first time, it is possibly rare information. I find it hard to believe myself