Can depression cause your whole face to break out?

No, not directly: Depression is often awful. But it gets about as bad a rep as it deserves. It can upset several physical systems and can make our behavior patterns - like hygiene, eating, sleeping, etc go out of wack and the combo of these can perhaps mess up your skin. But that being said - if it takes breaking out to get you into treatment for depression - fine. Do find a therapist and be evaluated and treated.