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C~
In addition to the suggestions Victoireh offered, you may want to consider a mucus clearance device. One example is the Flutter Valve. These devices vibrate the airways as you exhale to loosen mucus, making it easier to expel. Used daily, it can help to keep the lungs clear.
I've suffered a lot of sinusitis in the past, and it does drain down the back of your nose into the top part of your trachea, where you cough it up. You really should be using a steroid nasal spray for you excessive mucous production for your sinuses. Antibiotics help acute sinusitis infections. I often do saline irrigations of my sinuses, that helps remove the excess mucous that is in the sinuses. Also gets rid of infected material. These irrigations should be done twice a day. I've also noticed that when you have excess lung mucous you will feel it rattling around deep in your lungs before it makes it's way up. Plus the mucous from the lungs is much thicker and stickier and harder to cough up. But sinusitis does aggravate asthma quite a bit, and a lot higher dosage of steroid inhaler is required to control the asthma. It is good to get your sinusitis properly dealt with.