Should i give my baby vitamins?

My baby is 20m old and is constantly getting sick. Mainly throat infections bc he's always putting crap in his mouth! He's sick mayb every other month its overwhelming I feel so bad for him. I try so sanitize and keep everything clean but there's just so much I ca do. I was thinking of buying him the gummy vitamins. Do you think it'll boost his ammune system? He's a superrrrr picky eater and doesn't eat many veggies :/