I would like to start Ballroom, and I would like to compete ultimately. I am interested in waltz and fox trot mainly, but my question is do I have to learn the international style in order to compete? the places where I am thinking about taking lessons don't have a lot of international style classes, mainly american style, is it still ok to good even if i wanna compete?

There are competitions in American style. Generally though someone who really knows what they are doing will be able to teach both - there are many pros who choose to compete in american style themselves, but pretty much all of the good ones have international style students, often even students they do pro/am competitions with in international style. Latin and rhythm have some real technical differences, but smooth and standard are just two applications of the same set of base skills.