You can check historic wait times at immigration here:
http://awt.cbp.gov/

Calculate the max wait time at the AA terminal (as a non citizen without global entry this is not unlikely) of around 30 to around 100 minutes.
Add the time to retrieve your luggage, go thru customs,
Consider that you need to drop your luggage before the cutoff time (not sure how long before the flight departs) or make your way to the QR check in and check in before their cut off.

3 hours seem to be doable, but don't leave much room for things to go wrong.