Because most X-ray machines nowadays are digital, the hospital should keep them for a while as long as they are not too old. You can contact the other hospital, or through an intermediary (the organization responsible for contacting the medical examination) to let the other hospital to reprint or develop a new one can be. Of course, nowadays not every medical equipment in American hospitals is very advanced, and in extreme cases, there may be old optically-exposed camcorders, and that can't be helped.
However, if you can't find it, it's not a big problem. X-rays are basically the same in China, and you can't be sure that you'll be able to find a third-party hospital to take them.