Side affects are rare- my hubby get's them (so he was told not to get the shot again after the 2nd reaction he had to it), so I was a bit concerned when LO got her first flu shot last year- but our oldest has no reaction, and neither did LO.
I'm sure your LO will be fine. I'm on the fence this year tbh-- but prob will do it just cause it's one less thing to worry about, and last year my LO and I were sick enough with bacterial infections and pnemonia! If we'd had the flu too! Yikes!