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 second common cause would be nasal allergies, which are commonly causes this time of year by indoor allergens like mold, mites, and the like. In addition to itching and nasal mucus, there may also be frequent sneezing, nasal congestion, or eye itching or redness.