Is it possible to receive a U.S. health service scholarship at a carribean medical school like MUA, AUA (none of the big 4)? Especially if you plan on practicing in a state that's approved, like Louisiana?
Assuming that you are referring to the National Health Service Corps, the answer is no. From their bulletin:
Schools and Programs Must be Located in the U.S.
The schools and educational programs for which scholarship support is requested must be in a State (includes the 50 States, the District of Columbia, the Commonwealth of Puerto Rico, the Commonwealth of the Northern Marianas, the U.S. Virgin Islands, the Territory of Guam, the Territory of American Samoa, the Republic of Palau, the Republic of the Marshall Islands, and the Federated States of Micronesia). Students attending schools outside of these geographic areas are not eligible for NHSC scholarships, even though they may be citizens of the United States.