Limping behind an EP limper is okay here at a passive full table. This is 6-max though, and limping becomes reasonable much less often, as aggression is more rewarding in 6-max simply because more pots will be HU and the less players there are at the table, the less likely it is that anyone has anything worth shouting about.
You raise here to take the initiative with a moderately strong hand in position against someone who has shown no real strength thus far. At a very loose-passive table limping is okay, but as you haven't specified any table conditions I'm gonna assume it's just another standard $50NL table, in which case raise
Flop/turn is horrible. I mean, it's really, really horrible.
You have the second nut flush. There's a nice, co-ordinated board up, and thus there's a distinct possibility that someone has either a made hand or a draw that they're willing to go with. Make them pay! There's also the "someone either has the Ad or they don't but slowplaying is bad either way" factor - if someone does have the Ad you're giving them a free shot to beat you, and if they don't then a diamond turn/river is going to absolutely kill your action.
You identify you "probably should have raised" the turn, but the flop is just as bad, if not worse. Get someone with the Ad to tag along without odds
, get some money in with the second nuts on a board that's probably hit a lot of hands, get some money in before a card comes that kills your action!
As played, probably fold the river, although I don't hate calling. You should never have had to make the river decision though - there should either be so much in the pot that you have to call, or everyone should have folded already.
Oh, and don't sit with $16 at a $50NL table.