What happens when there is not enough of anything, which in this case would be Doctors?

The free market fills the void. There are Doctors overseas that would love to come to the US if they could get the work Visa. If they can make a better living here than over there.....

Still confused about how this works? Read a book by a fellow called Adam Smith. I think the title is 'The Wealth of Nations'. Pay close attention to his treatment of the theory of the Invisible Hand.