I’m trying to give your country the benefit of the doubt. Every source I can find says that most Portuguese use the correct Americano/Americana terms. If you insist that your country is full of the willfully ignorant, I will not argue it.

So for you, American means only someone from the US

Not for me, for the majority of the world. American has been used to refer to people from the United States of America for nearly 300 years. To be upset about that now is just asinine.

but we can't mention someone from the US as north-american

You can, but it does not refer to United States citizens only. It refers to everybody in the United States, Mexico, Canada, and technically speaking almost two dozen other countries and states. You need to understand the difference, this is not a difficult concept.

I just said America is a geographic place that you are trying to prove it doesn't exist

“America” is a short name for The United States of America. It is the only country on the continent with “America” in the name. Which is also why United States Citizens are known across the world as “Americans”. It is distinct to them because it’s part of the name of their country. It is not an actual geographic place.

The United States of America is a country, which is located on the continent called North America. There is no such place as just “America” here. In most English speaking countries, or around the world. The small fraction of foreign countries who have a crude and primitive understanding of North American geography are really not a factor. Imagine if everybody in North America got together and decided the demonym for the Portuguese was “Peepee poo poo people”. Would that make it so for the Portuguese just because a bunch of us on a faraway continent decided it was? Probably not, I’d imagine you’d still consider yourselves Portuguese.