Some are available by prescription only. You might have to balance strength versus drowsy side effects. Zyrtec, a newer antihistamine for children, usually works very well while not being very sedating. The simplest anti-itching compound is a paste made of baking soda and water. Use just enough water to make a sticky paste, and spread it on.
Calamine lotion works in a similar way, and usually the effect lasts longer.
Other children prefer a menthol lotion such as Sarna. Topical steroid creams of various strengths can also be useful. Occasionally reactions to mosquito bites can be severe enough to warrant systemic steroids. You might find both of these in a health food store. Probably they will instead get better over time.