Augmentin is an antibiotic. it slowly kills the infection. But for pain relief you need to give her paracetamol or other pain killer. For the tonsils, once the infection is resolved you can consult your ENT doctor for advice on surgery, he will tell you if you need surgery based on after taking history and examining your daughter.
Next Steps
Betadine in saline gargles are helpful. If you child can gargle, you should give a try.
Health Tips
If the symptoms are very frequent , then you can go for tonsillectomy.