Should I move to a different country and leave my family behind?

I live in an Eastern-European country with my parents and grandparents from my mother's side. My goal is to move to the U.S.A after I finished college, and collected enough money. I want to pursue a career in art, either as an animator, or a cartoonist, or a graphic designer, or as an illustrator, etc. Plus, I understand and speak perfect English, with no trace of an accent. I also know the Pledge of Allegiance by heart. I work and study hard so I could make my dream a reality. I even pulled multiple all-nighters to study or hone my skills. My talents are wasted here and I want to put them to good use. Every teacher, mentor and friend I've had agreed with my dream and fully support it. Problem is that my family isn't supportive. They want me to stay here, get married soon, and live with them. Made worse by the fact that they're not exactly in the best of health. They have problems with their knees, backs, bones, joints, etc. On top of everything I just listen, we also live on a farm and there are animals to feed, wood to chop, a big garden to take care off, etc. I don't know what I should do. Should move out, put my skills to good use and start a new life with a family of my own? Or should I stay here, take care of family I already have, and leave my dreams in the dust? I need help.