American English: "come down with something"
You most often use this expression to say you are getting sick with an illness likely caused by a virus, such as a cold, the flu or the stomach flu.
Did you come down with a cold often this past winter? Lots of us @educhora certainly did. You bet we're glad spring is here! But ever sanguine, we're also happy to have (re-)learned the importance of washing our hands often. See, Kindergarten does matter! (You may be interested to know that there is at least one person working @educhora who is a Kindergarten dropout!)