Take the NY Airporter bus to JFK on rush hour it will take you maybe an hour, generally AA will be the last stop, now there is construction on the Van Wick south, down by exit 5 till exit 1.
A cab shall cost about 30 dollars, might be a bit faster.
Flights to EZE close 45 minutes prior departure.
You will have little connection time.
Perhaps try ORD-DCA-JFK, or ORD-bdl-jfk or ord-pvd-jfk

btw AA is on 763