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.
(Mucus can also form in the lungs, which is the case in patients with asthma and chronic bronchitis. When that happens nerves in the bronchi are stimulated, resulting in cough.). Mucus dripping from the nose or sinuses is called post nasal drip (PND). PND is the most common cause of chronic cough. If mucus stayed in the nasal passages and sinuses -- if it did not drip into the back of the throat and down toward the lungs -- then rhinitis and sinusitis would be an uncommon cause of cough.