Can prednisone help with blocked sinus passages?

Yes, carefully. Prednisone is sometimes used when other treatments have failed. A large part of treating sinusitis is treating the inflammation, so the lining of the sinuses can shrink and the sinus can drain. Prednisone is also used to shrink or control polyps. It is not usually a long term solution. See an ent, especially if this treatment has been recommended repeatedly.