It is quite possible your cough is due to statins. Back off Lipitor and related statins. I am aware of several people tht did and the cough went away.
If your Dr. wants to keep giving you more antibiotics then maybe you should get a second oppion before you end up in the hospital with pneumonia. That stuff is serious so you better get it checked out. Good luck, I hope I helped.
After a month I'd be concerned about pertussis, as well as pneumonia. Ask for a chest xray. and perhaps some inhaled steroids or even oral steroids.