Reading your post, I see three things right away. “Exceptional student”, “international”, and “need full aid”.
I also wonder what you are thinking about for a major. Are you thinking of CS or some form of engineering? I am wondering about this due to your robotics interest.
I think that you apply to a small number of top schools in the US that meet full need for international students, and you apply to safeties in your home country.
MIT and Stanford are obvious if you are interested in computer science. I wonder about Harvard. It is not as well known for CS or engineering. However, it is trying to expand into these areas, it could use some top students in these areas, and it can afford to give good financial aid.
Carnegie Mellon is a great university for you except for one big problem: “International students aren’t eligible for financial aid at Carnegie Mellon”.