I think you played it well, but I would like to know your read on what SB 3-bets with preflop. That could make a difference.

Also, don't you have 8 outs on the flop? (Ax3, Jx3, runner-runner flush, and runner-runner straight). Regardless, I'm raising the flop.

I may have taken a shot at it on the river. This would totally depend on your read of the SB. If you thought he was capable of 3-betting pre-flop and then leading on the flop with Broadway non-paired cards, then I would bet the river. Usually, however, I would call the river like you did.