If your home has high concentrations of radon there are ways to reduce it to acceptable levels. Most radon problems can be fixed by a do-it-yourselfer for less than $500. If you want or require the assistance of a professional you may wish to look at the list of certified radon mitigators for your state.
Interestingly enough, one common cause of bloody mucus in nose areas is high blood pressure. While the blood vessels and the nose seem hardly related in any pertinent way, Kaiser Permanente points out that high blood pressure can cause nosebleeds, which can result in bloody mucus discharge. What can cause this is the perfect storm of adjacent occurrences.
The patient gets used to it, yet they are driving those around them crazy with the constant throat clearing. There are two possible causes for the problem you describe: chronic rhinitis or acid reflux. The first is a problem with the nose and sinuses causing excessive mucus production. The upper respiratory tract - which connects the nose, sinuses and throat - is lined with a wet membrane covered in cells that secrete mucus.