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.
Nasal Drainage-Post Nasal Drip. Glands in your nose and throat continually produce mucus (one to two quarts a day). Mucus moistens and cleans the nasal membranes, humidifies air, traps and clears inhaled foreign matter, and fights infection.