Not enough information to give you a definite answer. I wouldn't recommend spending the $300 for a new IAC on speculation.
Perhaps you can arrange to borrow one from someone to see if it helps or not?
I would also suggest replacing the 02 if the wiring is damaged since it's a critical component for maintaining proper A/F. Although it's also an expensive part I wouldn't hesitate here since it's already damaged.
Do you have any CELs? It would be helpful to hook up a scanner, or preferably a Delta Dash, and see what data is coming back from the various sensors.