Anytime you get a "mosquito bite"...the little red bump....it's an allergy to what mosquito "spits" into you. I don't swell like that anymore..don't know why I used to when I was a kid but I don't think I have since I had my children 20 yrs ago. Anyway....I suspect your child is "more allergic" then most people. Like some people can die from being stung by a bee -- others it barely affects.
Anyway....after all that I agree with what the others said....benadryl and make sure you're using off or some kid of repellant if you know she's going to be around mosquitos (that's a good idea with West Nile and other diseases that are spread by mosquitos.