Causes of Nasal polyp. A nasal polyp is caused by chronic inflammation of the mucous membranes lining the nose and sinuses. Nasal polyps are often associated with allergies and cystic fibrosis.auses of Nasal polyp. A nasal polyp is caused by chronic inflammation of the mucous membranes lining the nose and sinuses. Nasal polyps are often associated with allergies and cystic fibrosis.