By any chance have you a while ago suffered through a common cold? By any chance did you eliminate it? Of course you survived it! You cannot heal a runny nose itself, but your immune system normally establishes resistance to a particular cold virus within a few days. We call that healed by your personal immune system!

Parents have previously had a lot of the runny nose viruses. Parents have acquired resistance to the colds they have had. Therefore there are not quite as many cold viruses remaining for grownups to acquire. That is why grownups just succumb to a few runny noses per year whereas children succumb to a dozen colds annually.
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