"I have a New York medical marijuana card and buy my marijuana in New York."
No. Airport Security is are under Federal Control. Although the Federal Government doesn't have regulations on transporting marijuana, possession is a crime under Federal law. It is classified as a Schedule 1 drug. The U.S. does not currently accept its medicinal use making it illegal to fly with marijuana in carry-on or checked luggage. Also, it's prohibited to transport marijuana across state lines.
Each medical marijuana state has different regulations for transporting cannabis within that state. Currently, transportation of cannabis across state lines, including internationally, is not legal.