I was playing in a live 1-3 game, 9 handed from the small blind with pocket threes. The UTG limped and a mid player raised to ten and three other came in. I was a mid stack with $285.00 and I called with my threes as a speck hand. We ended up with six in the pot. The flop came 9 8 4 rainbow. I checked planning to fold. The hand checked around and a three came on the turn giving me a set. I chose to bet small hoping to rep second pair or draw, hide the strength of my hand and build a pot. My $15.00 bet into a $55.00 pot resulted in the UTG player raising to $30.00 and two callers. I now had a delema, a flush draw and couple straight draws existed. $150.00 in the pot. $240.00 behind with three opponents. I could reraise with my set (at least $100.00), which might cause a calling chain, or over bet to try to take it down. I decided to try to end the hand right there and pushed. The UTG called for less with a higher set.
Did I make a terrible mistake? If so at what point did I actually make it and how should I think about this situation in the future.