Here there is a saying that if you don't treat a cough it will last 14 days, but if you treat it, it will only last 2 weeks.
While a cough/cold can not be cured, it can be treated and kept to a point where it is hardly noticable. The advice given so far has been excellent. And be certain you do not neglect the garlic. Garlic is very high in selenium and gives a big boost to the immune system To get full use of it, use it in every meal. Do not worry about the neighbors, just chew on some parsly sprigs throughout the day and the neighbors will not even be aware you been munching on garlic.
So first priority lots of garlic, and more garlic.
Now that the immune system is kicked into gear from the garlic, concentrate on comfort. Honey and lemon juice seems to be best, in my opinion. But, also sipping on hot tea is very helpfull, if you have a touch of Moroccan in you or just like Moroccan food, Mint tea made like they make it in Morocco is great.
Also hot soaps through out the day.
So the formula to follow:
Garlic
Honey and Lemon
tea
soup
No specific order, just some of each several times during the day. Do not neglect the regular meals, all that is in addition to the regular meals.
Now, while this will, not cure the cough it will soothe it and very quickly rmove the symptoms. But even after the symptoms end, keep treating it for at least 2 weeks.