Nightingale syndrome 

The Florence Nightingale effect is a situation where a caregiver develops romantic feelings for their patient. Many often misunderstand the term to mean the opposite; that is, a patient falling in love with the caregiver as a result of interpreting an amiable bedside manner as affection.

See Florence_Nightingale_effect on Wikipedia, often confused with Nightingale syndrome (which is something else entirely).

Nightingale syndrome by Walkman100 January 19, 2016

Nightingale syndrome 

Based off the "Nurse with the Lamp", Florence Nightingale was apparently an extremely adept nurse. While not technically a medical syndrome, Nightingale Syndrome is known to be used to describe the situation in which a patient falls in love with his/her medical caretaker due to the vague bond created when healed by a complete stranger.

Karyn fell for her surgeon, can you believe that? All he did was patch her up after a gunshot wound to the stomach. What a textbook case of Nightingale Syndrome.

Nightingale syndrome by Marvin Wong. March 22, 2005

Reverse Nightingale Syndrome 

When a caretaker falls for the person they're caring simply because they sympathize toward them or feel more connected by that temporary bond.

My friend fell for me as he prayed everyday because of my Hypokalemia and messed up stomach. He later told me it was Reverse Nightingale Syndrome.

Reverse Nightingale Syndrome by 2213 April 13, 2011