Are people with cushing's syndrome ever prescribed antidepressants for the "losing my mind" feeling of hypercortisolism?

It depends: In "mood disorder due to a medical condition, " there's a clearly perceptible mood disturbance (either depressive or elevated, expansive mood) that causes clinically significant distress/impairment in important areas of functioning. It's physiologically related to the underlying medical condition, which needs primary treatment. Antidepressants & other meds may help manage symptoms in meantime.

Steroid depression: Yes, antidepressants are often used to treat the psychiatric manifestations of cushings syndrome. Most effective, however, is to cure the cushing's syndrome, usually with appropriate surgery.