Should you have shoved, yes I think so. To answer your other question on could you have done anything differently, yes you could.
Fold the hand pre. I know this hand can do well with a nice flop and it is a cash game, but with your stack I don't think you should be calling 6$ from your 54$ stack with 3♥5♥. Maybe you're a looser player and just want to have some fun, that's fine but you didn't need to play the hand. You never mentioned your position directly, but said someone was in an earlier position from you so I am assuming you limped or are the BB.
You could have also donk bet it after flopping so big, your hand is disguised well, so even if someone shoves you don't mind calling, if they call you see the turn and can reevaluate, or they fold and you win a 24$ pot. You're playing 3♥5♥ for this type of board.
You could even have open shoved. Increasing your stacking by 50% is not to be sniffed at, happily steal that and maybe not show down. Maybe not the best move in some games but this one really depends on the players at the table. If they love calling with top pair why not just push it in? It's hard to bet fold here with your stack. After you bet and if it's called you don't really have a meaningful shove left against a big stack. This point is very dependent on the players at the table though.
In the end you got unlucky that they hit the open ended draw, but you could have done a few things differently. Whether point 2 would have changed the result is something we will never know. Once you see that flop with that hand and the way you played it yes your money is going in.