What Causes Chapped Skin Under Nose?

My daughter has had a very dry, chapped skin type of rash under her nose for awhile. I took her to the doctor and she was diagnosed with impetigo, but she has had no blisters or itching so I am questioning the diagnosis. She was prescribed an antibiotic and a toptical ointment. It's been three days with no real improvement. should I seen another opinion?