A cough following a head cold can last for about 2 weeks or so. If the mucus is clear then it is not infected which is a good thing.
If there is postnasal drip trickling down the throat then use of an antihistamine plus a cough suppressant(dextromethorphan) will relieve the symptoms. A Robitussin combination should be helpful. Some will make you drowsy so don't drink alcohol or drive with these.
If the throat is tickly then a syrup based cough mixture will sooth the tickle, glycerin is good in this case.
If the mucus starts to become more troublesome, or the chest feels like there is something 'rattling' then an expectorant such as gauiphenesin will help.
Other things to do include drinking plenty of water (2 litres or 4 pints per day) and steam inhalation twice a day if there is mucus in nose or chest.
I'm afraid that this is all you can do to help the cough. It will get better with time. If it lasts for three weeks then see your doctor.
Best wishes
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