NL200: TT set on river when flush comes in

[Jurrr]

6-handed. Hero is UTG with T[img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/heart.gif[/img] and $200. BTN is 37/11/2.2 over 54 hands and covers, probably a donk.

Hero raises to $7, BTN calls.

Flop A[img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img] ($17).

Hero bets $14, BTN calls.

Turn J[img]/images/graemlins/diamond.gif[/img] ($45).

Hero bets $45, BTN calls.

River 7[img]/images/graemlins/spade.gif[/img] ($135).

Hero shoves for $134...?

This is because I don't feel like folding on the river as I think he will bet AT/A5/AJ/A7/55/AK/AQ often enough and to avoid a negative freeroll where I'm mostly playing a big pot when beat but he checks behind when he has a weaker ace.

Looks good or did I get it wrong?