Hi,
I hope that by now you have consulted your doctor about this matter and that your daughter is already on antibiotics. This is low dose of antibiotics and it should be taken daily as your doctor has prescribed for your daughter’s condition. These antibiotics have really low side effects so you shouldn’t be worried about that. And the kind your doctor is going to prescribe depends on her age, weight and allergies if there are any.
This treatment has a purpose to stop hydronephrosis from causing kidney infections. Since your child is diagnosed with mild hydronephrosis I believe there is no need for the surgery but of course you need to check this with your doctor to be absolutely sure. I hope that your daughter is going to recover very fast.