A long time ago in Japanese school I was told there is a old Japanese saying/諺 that meant "You can get rid of your cold by giving it to someone else."
Does anyone know what that 諺 is?
I have heard such a saying several times, but it's not regarded as a traditional proverb. It's more of a recurring joke, or a well-known superstition at most. I think almost no Japanese people seriously believe this. Perhaps you can google with 風邪は人にうつすと治る for more about this (this is not a fixed phrase, and no dictionary contains this).