Hi, today I got punched near the edge of my mouth unexpectadly. My upper lip is now cut pretty deep around half a cm. What can I do for it to heal fast?

Several things: hold. hold pressure=slow bleeding/allow blood clotting to seal microvascular leaks, clean tissue gently/thoroughly with soap/liquid detergent ASAP in 1st hours. Approximate edges; accurately as possible; internal sutures applied with skill best yet surface adhesive strips ("Steri-Strips") work as well/better for some wounds. Apply Neosporin once daily & cover with dressing/band-aid to suppress bacteria.