Likely have you hitherto had a cold virus? By chance did you heal from the cold? Naturally you got over it! You can't cure a common cold directly, but your body usually develops immunity to any cold infection within several days. We call that healed by your own immune system!

Adults have already had a lot of the rhinitis infections. Adults have developed immunity to the colds they have suffered from. So there are not quite as many cold infections around for adults to become infected with. That is why grownups only get infected with a few runny noses per year and youngsters succumb to a dozen colds annually.
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