I'm evaluating hand for my NL BSS Beginners Course.
Pre-flop: I would also raise, I can't see a reason why, unless the BTN is a maniac that plays every hand, so it's cool he calls, so let's see what the flop brings.
Flop: Just because you have the initiative, I would standart C-bet 2/3 of the pot so he is not getting the odds to chase the flush draw if he has one.
Turn: Ok now you hit a TPTK, it's cool, now we have an actual hand so we can keep firing, the only thing that beats us is an overpair and a 3, so 3 we clearly don't put in his range. Set of 55? Nah he wouldn't have bet the flop if he flopped the full house, so the only thing we need to worry about is JJ QQ KK AA, we can put him on JJ because those he would have called QQ KK AA he would have 3-bet pre-flop, unless he is really passive.
River: Now you pot it, and who can call you here? Basically only an overpair to your TT would call the pot size bet. I would have bet smaller like 1/2 pot because we want value and we do think we have the best hand. But he shoves all in and you are even considering not calling? Those 43c is nothing to a 3$ pot, and we beat most of the hands, so not calling here is not an option. So what did he have? You sound kinda sad, so it looks like he beat you if you are questioning your call. Did he had the JJ?