Yes. Inflammation is one of the secondary effects of allergic reactions. This usually happens latter after the itchy, sneezy, drippy drainage phase is passing.
Yes. Allergic rhinitis is by definition a condition in which the internal structures of the nose become inflamed. When allergens enter the nose, histamine is released at the molecular level, triggering a cascade of responses, including edema of the turbinates, mucus production, and general inflammation of the mucosa.