To get rid of a nagging cough that won't go away try taking some Halls Cough drops and take A hot steamy shower and also use a humidifier or vaporizer to add moisture to the air.
You can also drink some warm tea with honey as honey is a natural cough medicine and works wonders at getting rid of coughs.
Another way to make a natural cough suppressant with tea is to take some warm tea and add 2 tablespoons of honey and also for this cough suppressant you add some black pepper to the tea and honey which will make an even better natural cough suppressant.
You can also try putting your face near a Vaporizer or humidifier and breathing in the steam but be careful if you're near a vaporizer to avoid getting burned.
You can also boil a pot of water on the stove to put out steam and carefully breathe that steam in as well.