Why does my nose run when eating pepper?

Good question. There are three nerves in the nasal lining. The sensory nerves are stimulated by the pepper. Then there is a reflex arc to the central nervous system (brain) and the pathway back to the nose then stimulates the mucous glands in the nasal lining, resulting in the runny nose. The nerve in the nose causing the drainage is the vagus nerve and is part of what we call the autonomic nervous system.