I think you played it pretty poorly. The CO three-bet you before the flop, and the button cold called the three. You gotta figure the CO at least has a pretty strong hand, likely better than your jacks. Now when he cold-calls your flop raise, that should have been a signal to you that he probably has an overpair. I'm not sure why his three-bet and then cold-call didn't slow you down at all. Nice raise on the turn when the board paired, apparently raising for value with the third nut flush draw
Bottom line, you grossly overplayed your hand, and in all likelihood sucked out big time. On the off chance you were actually ahead, don't let that reinforce your play here - the vast majority of the time you're gonna be a big dog.