My daughter is, like you, very allergic to skeeter bites...they get all purple and huge and itchy. I happened to get a bug spray for my puppy when she was too small to put flea and tick stuff on her, that works for people too. It's called Dirty and Hairy Repel bug spray. It's all natural, smells pretty good too. I have asthma, and I can use it without an issue. Also, it doesn't cause any rashes, which is always a plus!

BTW, one thing I've found with my daughter, when she gets a few bites, I give her a Claritin and it prevents them from getting enormous and itchy. You might want to think about trying that.