Snap call that shizzzz, but your real error was not raising the flop enough.
When he bets $0.3 there, a potsized raise becomes a raise to $2.05 which offers 2:1. When you raise to $1.20 you're offering 3:1. If he has a hand like 98, he has a ~4:1 draw. So with your small raise, and you're prolly offering some implied odds
since its hard to fold sets, its not really that big of a mistake to call your small raise.
I'd pump his bet up to about $2.50, or even just jam all in. Fish are going to call you with a HUGE RANGE on this flop, and they're not going to fold draws at these limits. So charge them the maximum, because they will be calling.
And I call the turn shove because folding sets at 10$NL is bad.