I am an MD working in Manhattan. I just resigned last month, but my contract requires 3 months notice before I can leave. How can I get out of this?

You need to find a good employment attorney in NYC who knows whether the local courts will or won't enforce this provision of the contract against you.  The Courts do not like unreasonable provisions or provisions which prevent people from earning a living.  This is not my area of expertise but I can refer you to good counsel in this area. What is the basis for the 90 day notice period?  Is your former employer truly injured by your departure? Did you leave because they failed to live up to your contract? These are all questions you will need to go through with your counsel.  Hope this was helpful.