Psychosomatic

Psychosomatic illness or hypochondria describes a disorder that results from increased anxiety about an individual's health. Such patients believe that minor symptoms are indicators of a much more serious disease, or develop symptoms even without any underlying disease. However, sufferers still feel pain and other symptoms - the symptoms are not imaginary as is the case with Munchausen syndrome, the pain is quite real and is felt by the patient despite the lack of an underlying cause.
Physicians often have to reassure the patient that they are not really ill, but often this approach backfires as the patient sees the doctor as a source of sympathy and makes even more visits with new symptoms. Doctors will often try placebos which although they are untested against real disorders, will often allay the patient's anxiety. However, in severe cases, psychiatric care is recommended.
House displayed a large amount of psychosomatic pain in addition to his real pain after Stacy Warner broke up with him. Instead of injecting House with morphine, Cuddy used saline instead, which had the effect of lessening his leg pain.
In Brave Heart, House diagnoses Donny with psychsomatic anxiety regarding the premature death of Donny's father and grandfather when he can find nothing wrong with Donny's tests.  However, Donny collapses a few hours after he is released.
Arlene Cuddy demonstrates psychosomatic illness along with her real physical illness. 
Hypochondriasis at Wikipedia
Hypochondria at Mayo Clinic