Suggest Non Antibiotic Treatment For Cough In A Child

Hello Dr. I took my 10 year old son to the doctor today because he's been caughing for a week, pumping Albuterol every 4 hours. Dr. told me he has a sinus infection, so prescribed antibiotics, and told me to continue with Albuterol and also added steroids. I would continue with albuterol, but I would like some other alternative instead antibiotics. He never had antibiotics!
Thanks