You need an Antihistamine.
ie: Claritin, Allegra, Zyrtec.
This dries up, secretions.
Then, post-nasal drip, triggers the cough reflex as it drips down the throat.
Then, sometimes, post-nasal drip, can also infect the chest. Then a chest illness can occur.
I know, I had a common head cold. Post-nasal drip etc. Then, my chest got affected and I had by then, chest congestion (not nasal) and then, I got Pneumonia.
The Doc said, post-nasal drip, can affect the chest, too.
There is also Mucinex. Which thins the mucus. So that it can be expelled and reduce congestion.
Then, you can also with nasal issues, have a Sinus Infection. For that. Sudafed with "Pseudoephedrine" is good. But, you have to ask for it behind the pharmacy counter. It is 12 hour, non-drowsy. It will help. My Husband uses that, for his sinus problems. He uses that, and Claritin.
And he also, uses a Neti-pot to flush out the sinus.
If you present worsening symptoms or other symptoms or your chest gets worse, you best go to a Doctor.