Stand in the shower and breathe the steam. But don't put the water too hot or it will give you dry skin. So maybe stand outside of the shower so you can have hot water but the hot water doesn't touch you, and just put your face in to breathe steam.
And a lot of garlic. Garlic kills the bacteria and viruses in the lungs. The garlic oil will get into your blood and work to kill any invention anywhere in your body. You can get garlic oil pills if you don't like the taste of that much garlic. Cures infections in the lungs, sinuses, throat, ears, and probably anywhere else. I used it for years, it always works.
Dryness in lungs causes more irritation which causes more coughing which causes more dryness and more irritation. Breathing steam stops all of that. And the garlic to heal any little infection that might have been making it worse.