Jack High - No Good!

I called with Jack high for the first time in my life last night. Obviously it wasn't good, but it was almost good. It was a SB vs BB battle. I raised with J9o in the SB, BB defended. Flop comes 884, two hearts. I check, BB bets, I check-raise, BB 3-bets. Turn is a 2. Check-check. River is 5, no heart. I check, BB bets. I think for a long time, I think the BB has a busted flush draw, like 9 or T high. I call, and he shows me Q3h. Ooops, Queen high good sir. I made the right read, but didn't have the guts to raise the river.