Petroleum jelly is a great thing to apply to your upper lip and around the nostrils when you or your child have a runny nose. No matter how soft they try to make tissues, my son always had chapped sore skin when he had a runny nose, until I discovered this solution. I have also used A&D ointment with wonderful results.
A&D Ointment is actually a diaper rash medication you can find in the infant section of your grocery store. It prevents chapped skin the same way it prevents diaper rash, by forming an impenetrable layer between nasal drainage and your child's skin. There is a difference is cost and A&D ointment has a distinct smell that may be undesirable to some, so you may want to experiment before settling on the product that's best for you or your child. Although, the extra vitamin A & D does seem to help already damaged skin heal. It's surprising that these products actually last a while, even with constant wiping with tissues. Just two or three applications is enough to save my son's skin.
It should be noted that products containing petroleum should be avoided when using supplemental oxygen due to the fact that they are combustible.