`Nurse romances', almost always between a nurse and a doctor or surgeon, are quite common. I've found a site that implies they're a WWII phenomenon; can't be that, as this one dates to 1913 (as does this New York Times headline on the subject... ) The interesting thing about that is that professional nursing is not *very* old, not much older than the ninteenth century, and the status of sick-nursing previously was peculiar; all women were expected to be willing and able to nurse their families at home, and the poor if possible, but secular professional nurses were confused with camp-followers.
UWMilwaukee has a special collection of them, and a summary that also makes them a post-WWII phenomenon, but Hallowell Abbott is in the game for "the image of nurses and the nursing profession in popular culture, and the books that serve to reinforce not only popular misconceptions of nurses, but of women generally, and professional women in particular."
We have: a student nurse who doesn't want to graduate because her 'trained face' distresses her; her childhood sweetheart who broke the engagement because she washes male patients; a socialite nurse; a nurse who dies in saving an annoying old patient from a fire; a car-accident; a lame child right out of The Secret Garden; heaps of money and house-decorating; and a marriage with an indefinitely postponed consummation (but a happy ending). I'd call that a solid third of the evergreen cliches, and the prose is springy enough.
Project Gutenberg file #14506, The White Linen Nurse
So wrote clew in Fiction (20th c.).