Use a napkin to get that annoying itch on your nose. Wash your hands before you remove your contact lens. Drink lots of fluids. Dry aircraft cabins are particularly tough on mucous membranes so bring a bottle of water on board, or ask the flight attendant for one. On long flights consider using saline nose drops.
Smoke can also contribute to mucous membrane irritation so avoid it if possible.
Avoid people with colds. It's perfectly reasonable to move to an empty airplane seat if your row-mate is coughing and sneezing. Decongestants can help with nasal symptoms. My recommendation, though, is to use something that you've used safely at home. Best to bring the trusted remedy with you on all your trips.