Joi Dorei Byoutou

Main character gets fraudulently fired from a major trading company. He catches some disease resembling a cold and is treated in the hospital by a doctor who used to be abused a lot at school. The medicine does not help, so the protagonist blackmails the doctor to reveal the fact that it was a misdiagnosis to ruin her reputation. This way he makes her his slave during the hospitalization period.

[From vndbreview]