What will help dry swollen nasal passages? & what causes this?

Nasal saline spray: The first thing to try is simple nasal saline spray which you can get over-the-counter. Use it as directed. Also, there are some brands of "saline nasal gel" which can be sprayed or applied with a cotton swab to your nasal membranes. You might have allergic rhinitis or possibly some other underlying disorder causing the dryness. See your provider within a few days if the saline doesn't help.

Saline: Nasal saline is the best place to start. Over the counter by several brands (nasal/ocean/etc.). Likely due to drying in winter months. Vaporizer / humidifier could help as well. Start simple / holistic and work up to nasal steroid if not relieved.