Is the soreness inside your nostrils or on the outside of your nose?
If it's inside the nostrils, you may have a nasal infection caused by staph aureus germs. This usually produces pimple-like sores that pop and ooze yellowish, bad-smelling pus. Most of the time, you can clear staph aureus from your nose by applying a bacitracin or combination antibiotic ointment (like Neosporin). You can buy it without a prescription and using a Q-tip, apply a small amount inside your nostrils faithfully once a day for several weeks.
If that doesn't work, and you still are getting sores in your nostrils, see a doctor for some prescription-strength salve.