This could be from anything from bugs, dust, smoke, allergies to animals, plants, moulds, feathers chemicals
and so on. Even a
dry atmosphere can cause a
dry irritating
cough.
Antibiotics will only work if the problem is caused by bacteria.
Warm water with honey and lemon is good to soothe your irritation in the throat or a warm blackcurrant drink like Ribena (if you are not allergice to blackcurrants!