Cats do get "colds". They are subject to some strains of the same virus(es) that give us colds.

Cats can get dust alergies. Fifi once turned over a container of Cindy's foudation powder an got a "nose full" for her troubles. She would sneeze and then wiggle her head to clear it - only to have to sneeze on the very next breath. From a distance you could hear "Chew" - "Chew" - "Chew" - "Chew". She was so weak when it was over.

If your cat has not cleared up in 48 hours, yep, head for the vet.