Seems like a standard call to me. I think you have adequate outs to continue here. I'd estimate around 5.5 outs, and therefore you're getting the immediate odds to call on.

Folding the river unimproved is best, in my opinion, since villain will very rarely have less than TT here.

I don't like the check-raise on the flop, and think you should simply check/call here. The check-raise trapped you into an uncomfortable turn decision. As you mentioned, I think check/call, check/call, bet/fold would've been a more appropriate line. Had a blank fallen on the turn, I think bet/folding the turn is superior.