When you have a nose that is burning you can help stop the nose from burning by applying some moisturizer to the nose on the inside or where it's burning.
Neosporin can also help stop the burning of the nose and it's safe to put the Neosporin in the nose.
Using a nasal spray can also help stop a nose from burning.
Also use a humidifier to add moisture to the air which can help your nose stop burning because a moist nose does not burn as much.
If your nose is burning it could be because of an allergic reaction to something in the air that you're breathing in.
And using an allergy saline spray solution can help get rid of the burning sensation.
If the burning of the nose continues then I would recommend seeing a doctor about it.