How do you disinfect a nose piercing?

Take it out. Sorry - i know that's not the answer you want to read - but you have an infected wound with a foreign body running through the middle of it. Remove the jewelry, clean the skin thoroughly, and if there's a lot of pain, redness, firmness, and swelling, you'll need to get a prescription for an antibiotic. Once it's healed you may be able to replace the jewelry - but don't count on it.
Nose piercing. The easiest way would be to immerse it in rubbing alcohol - assuming the material isn't harmed by alcohol. Let it sit for several minutes and remove and let it air dry. Another way - if the material will withstand it - put it in a cup of boiling water and let it sit for several minutes. Make sure you do take the piercing apart.