Can chest congestion cause minor inflammation in the lungs because of post nasal drip?

It may.: The upper respiratory tract(nose, sinuses, pharynx) lead straight into the trachea and lungs. So if there is inflammation of the nose & throat, a cough may follow. You have listed Prednisone and sudafed. Prednisone may reduce your resistance to infection and speed osteoporosis but help with allergies and chronic arthritic pain. Sudafed may be drying to mucus membranes and maybe add to a cough.

Not likely.: Post nasal drip likely comes from the back of your nose and drips down and is usually coughed out or swallowed down your esophagus. If you get a chest cold, the inflammation comes first and then congestion from mucus production. This is then coughed out or blown out if in your nose. The post nasal drip usually comes after most of your congestion is coughed out or blown out.