Use google flights. Note that AEP is the domestic airport. Only a few domestic flights operate from EZE - most people going somewhere other than Ushuaia need to change airports. Also check JetSmart and FlyBondi. On the 31st there are plenty of flights.
Aeroparque Jorge Newbery (AEP) is BA's other airport. I flew out of there to Sao Paolo a few years ago on TAM airlines before it became LATAM. It handles mostly domestic flights but some international flights as well.
AEP is actually the busiest airport in the country and BA
Now regional flights are back to as far afield as LIM. There are plans to one day operate flights to MIA by Aerolineas... but lets see.