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Protip: You can prevent itchy skin from being itchy for hours by running it under very hot water for 5-30 seconds. (Don't burn yourself; I use tap water with some cold water, and turn down the cold water until it seems really hot.)
I recently bought a battery-powered tool that creates a brief pulse of heat in a small metal applicator, specifically designed for treating itchy mosquito bites. It works well!
In the case of the mosquito bite, there is the additional aspect of denaturing the proteins left behind by the mosquito in order to cause them to be less allergenic.