A person who's recovering from an illness is a convalescent. As a convalescent recovering from surgery, your grandmother would probably love some company to cheer her and help pass the time.
Convalescent, as an adjective, can describe the period of recovery or anything related to the process of returning to health, like a convalescent program of physical therapy or a convalescent ward at a hospital. As a noun, a convalescent is a person who is recovering from being sick. The origin of convalescent is the Latin root valescere, which means "to begin to grow strong."