Nasal Discharge After a Cold

My daughter, aged 5, has been suffering from a cold for 15 days. After treatment, the cold symptoms have disappeared, but she still has a runny nose every day. She has a lot of mucus when she sneezes and often blows her nose. She says it itches. She also has a cough and there are small pus spots on her tonsils, which are constantly protruding, indicating enlargement. She is in good spirits with no fever, but these symptoms have appeared. I bought Xinning Granules today and am not sure if she can take them. Please advise based on the above symptoms, what disease my daughter may have contracted? How should the medication be administered?
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