Completing premed requirements after Bachelors I'm thinking about applying to medical schools in the USA. Many medical schools require a two-year course in chemistry including organic chemistry and a year long course in biology, as well as requirements in mathematics and physics.

I have already satisfied the mathematics and physics requirements and a portion of the chemistry requirements during my undergraduate study. Are there any programs that will let me cherry pick classes to satisfy the application requirements?
Yes. At many (most?) universities in the United States, you can take courses as a non-matriculating student to get your premed requirements.