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Often times colds are caused by virus. The mucosal surfaces of the nose and eyes are intimately related can sometimes there can be a spread of the infection causing a conjunctivitis. Treatment is for the symptoms and cool compresses often helps with any discomfort.
Sometimes the infection can be caused by a bacteria, in this case antibiotics are helpful. If the discharge worsens, your daughter develops pain or worsening symptoms, she should be evaluated by her pediatrician or ophthalmologist.