I think this was my 2nd hand at the table so no real information.

$5 NL Texas Hold'em
Seat 10 is the button
Total number of players : 9
Seat 1: EricBruz ( $9.30 )
Seat 2: CrazyBabes ( $11.95 )
Seat 3: smasheur_ ( $1.79 )
Seat 5: royalhands1 ( $4.22 )
Seat 6: Chunyee ( $4.86 )
Seat 7: Gomzi ( $4.72 )
Seat 9: sharpest_1 ( $28.19 )
Seat 10: juss_FOLD_EM ( $10.14 )
Seat 8: MikeF1889 ( $4.96 )
EricBruz posts small blind [$0.02].
CrazyBabes posts big blind [$0.04].
** Dealing down cards **
Dealt to MikeF1889 [ ]
smasheur_ folds.
royalhands1 calls [$0.04].
Chunyee calls [$0.04].
MikeF1889 raises [$0.25].
sharpest_1 folds.
juss_FOLD_EM folds.
EricBruz folds.
CrazyBabes calls [$0.21].
royalhands1 folds.
Chunyee folds.
** Dealing Flop ** [ , , ]
CrazyBabes checks.
MikeF1889 bets [$0.50].
CrazyBabes calls [$0.50].
** Dealing Turn ** [ ]
CrazyBabes checks.
MikeF1889 bets [$1.30].
CrazyBabes calls [$1.30].
** Dealing River ** [ ]
CrazyBabes is all-In.
MikeF1889 is all-In.
CrazyBabes shows [ 9c, 9d ] a straight, six to ten.
MikeF1889 doesn't show [ Qd, Qh ] three of a kind, queens.
CrazyBabes wins $6.99 from side pot #1 with a straight, six to ten.
CrazyBabes wins $9.52 from the main pot with a straight, six to ten.

I put them on JJ after they called the flop bet as fast as they did. If they had the over pair of AA or KK they would've bet to keep me from potentially out drawing them. There was no way I could put them on 99 or a straight after just calling my bets.

Should I have just folded the river after they put me all-in?

cant really see how much the river bet was.. but nevertheless im calling with my top set there 100% of the time.