Corn starch baths help, and so does a paste made of baking soda and water. Try not to rub it in though, because the rubbing activates the itching. Put a dab on the bite, and put a bandaid on top. Or, if you have an anti-itch cream that can be used on kids (ask the pharmacist), put it on the bandaid and then place the bandaid on the bite with no rubbing.
If it's mosquito bite, it won't last long. If it's a spider bite or something from a biting fly, that may be larger and hot to the touch. I don't know what kind you have near you, but we get greenheads, deer flies and May flies (a version of the larger black flies common to New Hampshire) - their bites are much nastier and more painful. May fly bites can cause a huge welt - I've had them 4 inches across, very itchy and very hot to the touch.
You can try ice if she'll sit still for it. You can have her wear thin cotton gloves at night so she doesn't scratch it.
If there is any sign of infection - pus, a hard white center, or severe spreading redness (with or without fever), don't fool around with it. Same goes for a bulls eye ring or anything radiating out of it - be seen immediately.