Yeah maybe try cleaning out the IAC with some carb cleaner, that's nearly free. I would also make sure that the throttle body is shutting fully (if you just swapped it the cable could be misadjusted?)
And coolant needs to be fully topped off and bled of air to have a normal idle. So make sure it's full and there's no air in the system. You either have a bleeder or not, both are easy enough methods of bleeding air though.
The FITV makes the car idle fast when cold, so start the car cold with the intake arm off, put your finger on the bottom hole that's in the throttle body opening, it should have suction. Then when it warms up and the fan comes on, it should no longer have suction. If it does, then you have an FITV problem.
Oh and it never hurts to make sure your PCV valve isn't gummed up, that's easy. Vacuum lines, check them while you're poking around as well. They shouldn't be loose, old, kinked, or cracked.
Good luck