One of the film's major advertising taglines was the erroneous claim "The First Man To Become A Woman!" In truth, as the movie makes clear, others had undergone similar surgery earlier; Jorgensen was simply the first well-publicized sex-change case.
Christine actually received her diagnosis in Denmark, not America, from Dr. Christian Hamburger, and it was that she was very likely a genetic female. One of the reason she sought his advice was that she had not gone through a typical male puberty.