Hi Friend,
I am sorry i cant help you with the doctors name because they never tell you or put their name on papers or anything, but i can tell you how much it cost me in American Hospital in Nişantaşı.
Its around 120 $ for an adult person. I dont know how much is it for a child. And it takes about an hour for everything to be done. But i am not sure if they do the same things that they did to me or some diffrent checks for skill workers.
Sorry that my experience is not that helpful but atleast you know how much to pay
Good luck