Whatever political rhetoric around immigration has been over the past few years, the actual laws and procedures haven't changed much. I have a close relative who works with CBP and the biggest mistake most people make is to try to change their status while on a tourist visa. In most cases, the process has to be initiated in the home country of the petitioner, which in your case is Argentina. You're bound by the conditions of the visa type you enter with, so even if you enter as a tourist but actually intend to stay indefinitely and apply for residency, you could be considered in violation which is almost a guarantee of getting not only denied, but denied reentry altogether in the future. I believe there is a specific type of visa for petitioners (I don't remember offhand) and you might need to prove you can assume financial responsibility for your parent, etc.
Keep in mind, a lot also comes down to the person handling your case in the US, if one detail is off in your paperwork, some officers have no problem kicking you to the back of the line. My relative isn't like that, but I've heard plenty of stories.