Cold sores most commonly show up on the lips and are caused by the herpes simplex virus.
Sometimes cold sores are confused with canker sores or mouth ulcers but usually if you have a sore in your mouth it's usually a mouth ulcer or canker sore and is not caused by a virus.
Although in some cases cold sores can show up in the mouth as well as inside your nose and sometimes even on your chin.
You can use Apple Cider Vinegar or Toothpaste to get rid of cold sores but getting rid of the cold sore in your nose may be a little harder to do.