Pretty sure I was tilting when this hand came up (long night of thrashings). Worked out, but wondering if this is generally a poor play.

I have 99 in 3rd position and raise, guy in 5th pos. puts in another raise, folds around to me and I cap it.

Flop comes A and two rags (no draws). I lead, he raises, I 3 bet, he calls. At this point I plan to lead the turn no matter what hits and if he calls or raises, I'm done. My thinking at the time, "This guy either has AK or AA or he has something like KK or QQ and if I lead this turn, he is capable of folding the latter hands as I've represented AK or AA thus far.

Turn is a 4. I lead, he folds after running his timer down.

I probably would have just called the three bet. I like leading the flop. If a player has a monster there which AK or AA would be on a A rag board they will typically wait and raise you on the turn if they have position. A flop raise here smells alot more like an underpair to the Ace thus your three bet and leading the turn is a nice play in my opinion PARTICULARLY if your opposition is any kind of player at all that is capable of laying down an underpair to pressure.

What limit is this at?

I was playing 2/4.