What is the best medicine to stop coughing?

Codeine: But it is a narcotic and needs a prescription. There are several over the counter meds that may help.

Depends on cause: Depends on the cause of the cough. Many over the counter cough suppressants provide temporary relief but do not cure a cough. If the cause is a bacterial infection, you may need antibiotics to help cure the cough

Find the cause: There are many possibilities, including being treated with an ACE inhibitor, having the kind of asthma that coughs, having mild cystic fibrosis, having whooping cough, having any of a dozen other common things.