I've been using one of these $10 mosquito bite zappers for years. It's like a little stun gun – you hold the business end against an itchy mosquito bite and pull the trigger. It sends a little spark of electricity (it feels like a static electricity shock you get from walking across a carpet). I usually give myself about eight zaps and it stops the itching for hours. The manufacturer says the zapper suppresses histamines responsible for itching.
When I first got it, my kids were scared of the little shock. But they soon came around to the point were they happily self-administered the treatment.