There can be 2 explanations for this occurance.
I. Your child might be allergic to Augmentin
...if she has never been given this drug or amoxicilllin containing drugs before...then the treatment offered to you is justified.
2. Your child is suffering from Infectious mononucleosis
....a viral disease...these children develop typical rash
type of drugs are given....this rash will subside after the disease is over..there is no medicine for this disease per se...
In any case the treatment offered to you will be the same...I hope herrashes subside down. A better option is to go for blood tests to diagnose the disease.
Hope this helps you out.Wish her a speedy recovery