THere are a number of nasty bugs that can exist in water if it's not chlorinated right. If the water's chlorinated right, it should not smell like chlorine. If it does the chlorine's all gone and that's chloramines you're smelling. If the water's chlorinated right and on the high side, it will actually clear up the infections.
My husband is a chemist who specializes in water treatment. Honestly, I do not believe it was the pool water. Plus, there were the other kids who also had mosquito bites. I understand she could have picked her nose, etc., scratched and all. I guess my point is their point... this stuff is nasty. It is spreading rapidly. It is weird. And, BTW, this child has rarely been on antibiotics.