Sickness Unto Death(2009)

This is the mysterious story of Futaba Kazuma's first patient. At 18, Futaba Kazuma went to school to get his qualification in clinical psychology. While attending school, he boards at a creepy mansion, which even has a butler. Also living there is a strange young woman called Emiru. She is suffering from a terminal illness of the heart --- despair. This deep psychological problem has eerie physical effects as well: her hair has turned white, her body temperature is well below normal, and her blood pressure is also bizarre. No psychologists or counselors have been able to help cure her of this problem. Will Kazuma be able to determine the cause of Emiru's despair and save her before it's too late? [tethysdust]

(Source: MangaHelpers)