It sounds like mouth, hand and foot disease. It's a viral infection that causes a high fever and when the fever breaks it causes a rash on hands and feet, and sometimes legs and buttocks. It can not be treated but you can use over the counter medications to make your child more comfortable.
A 7 week baby girl is suffering from rash on her hands and feet, fever, cough and high WBC count. What kind of infection does she have?
You need to take your baby to a doctor, not wasting time asking people on this site .
You should be on your way to a doctor or hospital . Not asking people on a website who can possibly give you false information . Talk about being irresponsible..