Depends:
Productive cough........one that is producing sputum.
Non productive cough.....one that is harsh, irritating and not producing sputum.
If it is productive, then no cough suppressant is required and I agree with daffy, none is needed although cough medicines containing a mucolytic agent (breaks up the mucous) is often prescribed.
Non productive coughs can indeed be debilitating and interrupt sleep patterns and often follow virus infections and may last up to 6 weeks and it is in this case the patients often look for respite from the GP.
Over the counter "cough bottles " are of limited value unless of course, as in my first post, they contain an antihistamine which, by virtue of it's sedative effect may well be effective if the recommended dose is doubled checking of course that there is no drug interaction with any ongoing medication.
When she you see your GP for cough relief?
If you feel well, as in the case of the OP then one can leave the cough for up to 5weeks before seeking medical attention.
If you don't feel well, hot, sweaty, lethargic following a cold then you should see your GP after a period of 48 hours following the onset of this change in events.