Try following up yourself and being persistent. I had a really tough time getting people to reply back to my emails or to call me back. You just have to keep trying until you talk to someone. Of course if you've talked to them and they simply said they're not hiring that's a different story. Lastly you can literally call the anesthesia department of every hospital in the city. And like others have said you might have to start looking outside NYC and look into either upstate NY, Long Island, or NJ. you might even be surprised and get a better offer in the suburbs of the city. Look on gaswork as well. And lastly talk to your program director and even department chair a lot of times they will know of people hiring or will have contacts in the area especially since you're doing your fellowship in the north east which is fairly close to NYC.
Lastly, the job market isn't the greatest, I had friends who had a really tough time getting a job in NYC. Good Luck
