Removing tonsils in children: is it ok?

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I have 3 cute girls. The older one is 11 and recently was operated on to remove tonsils. She usually developed tonsilitis at the slightest taste of cold fluids, and it really used to bring her down with fever and all. She had a "bad" childhood for she never partook in ice cream and ice lollies like all kids love to. Now she enjoys them Well, the other girl, 4 years, is showing signs of having the same problem; and she really loves her ice cream. Could someone make me understand the repercussions of removing tonsils. Is it ok for a 4-year child?