Wrong. If you live over 180 days per year in Argentina, you must pay income tax here.Online work is a legal gray area. Technically you are not allowed to work as a tourist - at all. But if the work is not being done for a local entity, does that prohibition cover it? Logically, it shouldn’t; you aren’t competing with locals for that job, after all. And in practice, enforcement is all but non-existent - in any jurisdiction.
Taxes, as nikad notes, is another story. Technically, again, you are working here and should be paying taxes here. But you almost certainly won’t be paying taxes here, at least not until you have a DNI. So for all intents and purposes just assume that your tax situation will be exactly as if you were still in the US.
Once you have a DNI, you’ll have to decide whether you want to go the route of paying taxes here and seeking to reduce your US taxes as a result, or just continue as before.