6 month old coughing with phlegm

Hi, my baby girl is 6 months old and had started coughing about a month ago. We’d visited the pediatrician thrice but the medication given is standard and the doctor said that her lungs sound clear. However she coughs with so much phlegm, and often, she would puke while coughing. Could we seek your help to share with us some remedies that worked for your baby please? Thank you!