You can get an FAA (based on/restricted) license on the back of your IAA licences.
No need to get a freestanding/unrestricted one.
Your medical is valid for the unrestricted one as well.
Once you have that you only need a BFR and away you go.
No need for TSA/VISA etc etc
Biggest problem will be to get the paperwork sorted if your trip is before the end of next week.
Google FAA foreign licence
Good luck.