Expect costs of at least USD50,000/year to go to university in US as a foreign student. You must prove you have sufficient funds for all school + living expenses + return transportation to your country of citizenship to apply for student visa if a university accepts you. In the arts, of course, you will need art supplies, and they are not cheap. Also, if you are thinking of NYC, cost of living is extremely high, so don't expect $50k/yr to begin to cover costs there.
Financial aid for foreign students is scarce & extremely competitive. Do NOT expect any financial aid whatsoever for any fine arts programs. If you have won art competitions, use any monetary award for that toward schooling.
Foreign students are strictly prohibited from working in the US. Do NOT think you can sell your paintings in US, either. Work you do at home in Hungary over summer vacation & sell there could be used for school expenses abroad.