I have coughed for nearly two weeks and it is nearly gone. I only started to use medicine 感冒清热冲剂+京都念慈庵 this week and drink a lot of hot water. For me, it works.
I did some research on internet and was told that cleaning mucus is the main motivation to cough for human beings. They recommended to drink hugh amount of water to dilute the mucus so the cough may stop; or some medicine to restrain mucus may also be used. But usually, antibiotic doesn't work in this context.
I am not a doctor and so what I said is just for you reference.
PS, pay attention to contagion among your family members. Good luck!