Entering a professional school in the United States for international students who do not have a U.S. permanent resident visa (a green card) can be quite difficult. Many professional schools will not accept international students. Why? They recognize that your tuition does not cover the expense of training a professional. So they are investing in you. Their fear, often based on past experience, is that you could lose your funding midway through your training and their investment would then be lost.
Please note: Although medical and dental schools are often very restrictive about accepting international students, other healthcare programs are more open to international students. Law schools each have their own policies toward international students. They often require a TOEFL exam and proof of ability to finance a law school education.
Scholarships for medical training are rare and most American students fund their medical training with U.S. government loans, which are only available to citizens. Schools that do accept international students differ in their policies. Some mean only Canadian students when they say "international." Others expect you to have two–four years of tuition (between $40,000-200,000) in an account before you will be allowed to enroll.
Consider an MD/PhD. These programs are highly competitive but a few are more open to international students.
Secure a loan from a private bank. This will generally require a U.S. citizen to serve as a co-signer.
Consider an international medical school either in your home country, the Caribbean or another country.
Look into the International MD Program at George Washington University, a program designed for international students who would like to enter an American medical school but wish to practice in their home country.
If you are interested in international health, you might want to consider the Ben-Gurion/Columbia program, a collaboration between Ben-Gurion University and Columbia University focused on graduating doctors with special skills in primary care and community, preventative, and population-based medicine.