This is a short story by Catherynne M. Valente. You can read it online for free.
I don't have much to say about it: there is a little sex, but the story is mostly wonderful and melancholy and spooky all at the same time. It has an atmosphere excellently supported by the little details: "I wash my hands more than anyone on my ward", the dream, her job as opposed to her identity...
Go read it!
P.S. This story was brought to my attention when the author mentioned it was up for an award which the public gets to vote for. Here is the poll, which includes links to the other stories, I believe, and also the author's post, for those interested.