It is quite acceptable to list two affiliations in a paper. Typically, the purpose of listing affiliations is to make sure readers know where to reach you if required. So it would, in fact, be good to list both your grad school and your workplace as your affiliations. That way, even when you have completed your course and are no longer with the grad school, you will be reachable at your workplace.
Although there is no clear rule about the order in which to list your affiliations, it would probably make more sense to put the academic affiliation first as that is where you are getting support from for writing a paper.
I would also suggest that you seek permission from the hospital where you are working before listing it in your affiliations. Although they are not likely to have any problems, it is best to be careful as you wouldn’t want an issue to be raised after your paper has been published.