colds and phlegm.

My baby is just 5 months old. Earlier, my baby had a hot fever reaching 39.9. I have brought my baby to see a doctor. And, after 1 day my baby's fever has recovered after being given a fever medication. Two days later, my baby had a flu and cough, it was like there were a lot of phlegm in my baby's chest. I have brought my baby to see the doctor again, but only the nose drops are given. So now my baby is still coughing and still flu , it's been over 5 days. I am very worried. My baby is still breastfeeding. But I still worry when I hear my baby coughing and it will sound like a lot of phlegm in my baby's chest. What else can I do to eliminate my baby's phlegm and cough? tell me how can i know if my baby in a terrible flu. And what i shouldnt do while my baby got flu. i really need a help from expert mother or expert doctor. thank you so much.