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.
It is possible that the nasal cycle may exacerbate the nasal congestion caused by the common cold, as the lack of motility of the cilia in one half of the nose may lead to an uncomfortable sensation of not being able to shift mucus by blowing the nose.