Q3s in a multiway pot

[Jeans]

Poker Room skin
No Limit Holdem Ring game
Blinds: $1/$2
5 players
Converter

Stack sizes:
UTG: $132.75
CO: $243.75
Button: $197.00
SB: $121.00
Hero: $197.00

Pre-flop: (5 players) Hero is BB with Q[img]/images/graemlins/heart.gif[/img] 3[img]/images/graemlins/heart.gif[/img]
<font color="#cc0000">UTG raises to $5</font>, CO folds, Button calls, SB folds, Hero calls.

Flop: 4[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/diamond.gif[/img] ($16, 3 players)
Hero checks, <font color="#cc0000">UTG bets $10</font>, <font color="#cc0000">Button raises to $30</font>, Hero calls, UTG folds.

Turn: 9[img]/images/graemlins/club.gif[/img] ($86, 2 players)
Hero checks, <font color="#cc0000">Button bets $62</font>, Hero calls.

River: Q[img]/images/graemlins/spade.gif[/img] ($210, 2 players)
Hero ?

This was a really tough old hand I found in my PT database which I felt like I completely missplayed, perhaps I could fold preflop but let's not consider that option for now. On the flop I cleary see button has a strong hand, but with a draw I'm thinking maybe I can get UTG with me to the turn with huge implied odds? or should I just have shoved the flop? The turn is a blank, can I fold my hand here? And what to do on the river when I make trips? Perhaps I could just fold this marginal hand preflop to avoid this tough spot.