Exactly how my daughter reacts to mosquitoe bites; she's allergic to them.
Not much you can do. Give her Benadryl or Claritin--whichever one seems to help her the best; makes her the most comfortable.
We use a lot of natural products from Whole Foods, like anti-itch creams, and homeopathic remedies to help take down the swelling. Cold compresses will help as well. We also have an antihistimine we get from our naturopathic doctor that has worked wonders; takes down the swelling quite fast.
I've known some kids who have grown out of this allergy; so far, my daughter has not, and she's 12 years old.
You can also try putting Epsom salts in a bath, or try using Aveeno's oatmeal bath/nonitch for things like chicken pox, poison ivy/oak, etc.