Your daughter seems to be suffering from recurrent allergic cough and cold. Most of these episodes do not require antibiotics. Most often anti-allergic syrups and bronchodilators would suffice. Sometimes, if your doctor is reasonably sure that a given episode is a bacterial infection, then only antibiotics need to be given. Recurrent antibiotics may sometimes be associated with some side effects. There is no permanent cure for this, but the good thing about allergies is most of them spontaneously become better as the child grows.