How do I show others what I am capable of?
To apply for admission as an undergraduate at ... (MIT, Harvard, etc.) ... their web sites shows the steps you need.  There is an exam (SAT, Scholastic Aptitude Test) such applicants may take.  Probably there are opportunities to take it in your country as well, but maybe just in one or two cities, so you may have to travel there to do it.  (16-year-olds generally haven't published papers.)