Hia nd thanks for the query,
If your doctor has told tou that there is no sign of infection then your cough
is possibly a post infection cough.
The vocal cords are very sensitive. When they are injured due to infection they take a long time to heal completely, so you may be free of infection but since the cords have not recovered completely you continue to have cough.
Also everytime you cough you end up injuring the cords leading to more cough, its like a vicious circle that must be stopped.
All you need is a very good centrally acting cough suppressant like dextromethorphan
They are not available over the counter so meet your doctor for a prescription.
To get some sleep you can ask your doctor for sedatives. In general all sedatives are effective cough suppressants as well, so dual benefit.
Please follow some general measures.
1)Absolute voice rest for 4 days following which you can start talking a bit. No screaming or whispering.
2) Steam inhalation 4 times daily for 10 days.
3) Plenty of warm fluids.