Is there a such thing as an allergic reaction to mosquito bites?

My daughter ended up coming home from her grandparents house on Thursday with 18 of so bug bites on her body. Starting Saturday the ones especially on her foot were about the size of half dollars and bright red. She developed a fever of 104. We took her to the ER and they said that she had chicken pox. I dont believe she does. They are starting to go down now after an oatmeal bath and calamine lotion and her fever is finally going down after two whole days. Is there a such thing as allergic reactions to bug bites from mosquitoes? By the way my daughter has had the varicella vaccine.