Here is how I would of played it Sammy, rightly or wrongly.
I will try and explain my play as though i have not seen my opponents cards.
Its 4 handed and there was no raise to your BB pre-flop.
I would raise here.
Not sure if the button would of called the raise but the SB would of for sure.
Post flop you have hit your set, this is almost perfect for you.
You must get as much action as you can here, slowplaying is not the clever option here unless you can read your opponents like a book.
But hitting your hidden set on the flop in a limit game virtually demands that you jam it at this point.
I know you said you don't usually slowplay, and there was no reason to here, like I said, it was almost the perfect flop for you, but by no means perfect with possible draws showing.
By playing as described above, by the turn you will have gained some information from your opponent/opponents.
Again, here, I would raise any bet that might come from my opponent(s)
This is the point where you are gaining the most information available to you.
If you are re-raised, then you call.
By the time the river comes I would imagine it would be just you and the SB, the button would have to be into sado masochism to stay this far with the betting that would have ensued.
No point raising anything here as it looks like you are beat, so a check and/or call is the way to go here.
You have to call a bet here as you have nothing to lose apart from anthor $2.
In a sense you stumbled into your flopped set because you were in the BB and there were no raises pre-flop, I suspect this may have been the reason why you chose to slowplay it, and I can understand that.
So even checking pre-flop was no big error.
But when you flopped your set you need to think to yourself, if I was UTG and limped in with pocket 2s, what am I hoping for?
It was time to be aggressive, and by doing so it would of forced you to call the river almost regardless of the turn and river cards.
By doing so you would of won yourself a nice pot.
You may also of lost a nice part of your stack, but I hope you can see the advantages of playing this hand the way I described.
I sometimes struggle to get across what I am trying to explain in the conventional way but I hope this might help you in the future.