Is NYU's College of Arts and Science where an undergraduate should study in order to go to medical school?

First look at Medical schools in the US, do some research.

VERY few US medical school accept any  international students. And those that do, take in very very few of them.   So your chances of being accepted into any US Medical school after you have your four year Bachelor degree is extremely slim.

There are plenty of US schools that offer a pre med program for undergrads. I highly suggest looking in other states. NYC is crowded, VERY expensive. There are so many other areas of the US that are nicer.

Medicine is not a major for an undergrad. You need to pick a major and do the pre med program as an undergrad. Once you pick a major you apply to the college that the major falls under. You can email admissions office with any questions.
Make sure you are checking tuition and room and board costs.  There is very little financial aid given to international students from US schools