Depression is extremely painful. In my experience, severe physical pain doesn't compare to severe depression. There are many manifestations of this that go beyond "sadness and tiredness:" Hopelessness, emptiness, numbness, apathy, boredom, self-hatred, discouragement, loneliness, alienation, and a sense of being trapped/cornered off the top of my head.
"Homesickness" can definitely be a symptom of depression. The whole world feels very alien and hostile to me, and I commonly have fantasies of going to a place where things make sense and there are colors and I don't have to confront jagged edges everywhere.