Do you have to fly back to Argentina to renew your passport?
Can you go to an Argentina consulate to renew your passport?
Expedición o renovación de pasaporte (Pasaporte nuevo) 80 + 85*
The answer seems to be yes. However, in countries where there is an embassy and consulates definitely contact them first because it's possible consular services will only be provided by the consulate and not the embassy, strange as that sounds.
Your passport is expiring soon.
That's a problem, passport books are extremely secure documents and they are not printed by the embassy. They can issue a temporary one to return to Argentina but that can't be used to travel on. An ordinary passport booklet could take months for the embassy to ask the home office, get the home office to print it and get it to them. You need to call the embassy ASAP.