Does the timing of the flu shot matter?

My insurance covers flu and covid vaccines once every calendar year. I had them both January 2025, meaning I'm due this upcoming January.

However, I read somewhere that the vaccines really only offer protection for like 8-11 months. Is this true? Does that mean I have a gap of a few months where I'm not really vaccinated? I'm going to see a movie and am kinda freaking out that I'm just raw doggin flu season...