A cough is the throat's way of getting rid of something irritating it, but if the throat is infected it will not be able to cough out the thing that is irritating it. It will 'think' there is something there, and will automatically try to cough it up, so you get this annoying cough that doesn't get rid of anything.
Certain drugs, however, act as a cough suppressant, relaxing the throat muscles. Others loosen the lung passages. These are found in cough mixtures. Not simple cough remedies like Veno's, which you can buy in your local grocer's - these only soothe the throat, nothing more.
No, you have to go to a chemist's and get something with a 'proper' cough suppressant drug in it, e.g. codeine, dextromethorphan, psuedoephedrine. These things are habit forming, potentially addictive and have side effects, so a pharmacist has to be on duty. Examples are Benylin, Robitussin, Sudafed, etc.
Failing that, you should see a doctor.