What does it mean when my nose itches and runs and I sneeze a lot?

Allergy. To me it sounds like you have allergic rhinitis. The symptoms are very suggestive of that disorder. Your nose membranes can react to different types of substances called allergens. They cause swelling and redness and a lot of mucus. Pollens for instance are being attacked by your bodies immune system as harmful and causing a severe inflamation. Most of us have no problem.