Hi Smurf,
To play most places here you need a Matricula which is Argentine Association of Golf membership and they take care of the WHS.
To get your Matricula it's handled by each local club but you can walk into the Pro Shop at the Course in Palermo and speak to Marcelo pay him 285,000 pesos and you'll get your matricula number and first handicap which will be 54

, then you start putting cards in as usual.
This is valid for a calendar year so signing up now you lose 2 months already.
With your matricula number you can sign up to
https://www.adondejugamos.com/ad/reservasconsulta.php.and can play any of the opens that are available in the weekd.
Other courses are more private and you'll need a member to invite you.
Palermo you can play by signing up to a time on their vista golf website, but it does get very busy and can be hard to find a time.
Marcelo will explain how it works, I haven't played Palermo for a long time since moving to Pilar.
How your AAG handicap can be used abroad I don't know, I have never tried.
AAG website says you can though.