Good hand or good luck (3/6 LO8)

[adenosine]

I was playing in a local card room yesterday at 3/6 LO8, and a hand came up that I still question if I was doing the right thing. Any comments on my play would be greatly appriciated, as I'm still new to the game.

I'm playing in the big blind of a kill pot. The table is full of very passive players who will call you to the river with inferior hands, but generally they tighten up a small amount pre-flop with kill pots.

I'm dealt A 3 3 6 suited spades. I call a raise from a very loose player before me to see the flop. About 5 people end up seeing the flop.

Flop comes 3 9 J two hearts and a diamond.

The small blind bets, I raise. I know I can't get the low drawers out of the pot (they don't know the meaning of the word fold), but I figure I can make them pay to go for the low. Everybody calls.

Should I have been worried about 99xx or JJxx here? Both would have me drawing dead. I was prepared to throw my hand away if I got a reraise, but it didn't come.

Turn comes a black 10. SB checks, I bet, everybody calls. Should I have been worried here that somebody just made their straight?

River brings me a 10 of diamonds. I bet, everybody calls. Should I have been worried about 10 3 or a somebody who had a better set (seeing as I had bottom set), or would they have most likely reraised me? Should I have checked and seen if anybody did bet? I did have the fowest full house, and I would have had no way to know if somebody later bet with a straight, a better full house, or nothing.

What should I done differently here, if anything?