Slowing down?

[gmandan]

Party Poker 1/2 Hold'em (10 handed) converter

Preflop: Hero is UTG with J[img]/images/graemlins/spade.gif[/img], J[img]/images/graemlins/club.gif[/img].
<font color="#CC3333">Hero raises</font>, <font color="#666666">6 folds</font>, Button calls, <font color="#666666">2 folds</font>.

Flop: (5.50 SB) T[img]/images/graemlins/club.gif[/img], 7[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, Button calls.

Turn: (3.75 BB) A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, Button calls.

River: (5.75 BB) 3[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">Button raises</font>, Hero folds.

Final Pot: 8.75 BB

I'm thinking the two points where I could have possibly checked instead of betting was on the turn or the river since there are some serious scare cards that hit. There is no read on the player since this is one of my first 10 hands at the table. If I were to play this hand again, I would probably check/fold the river. Could I have saved another bet on the turn?