Inside my nose is very red and painful from the heat in my home, can i put neosporin up inside there to heal it, i'm afraid to use it incase it is dangerous to put inside?

Neosporin is a triple antibiotic ointment and is used to reduce the risk of infections following minor skin injuries. You don't appear to have an infection, but rather dried out mucous membranes from the heat and low humidity in your home. Speak to your local pharmacist re OTC products that can alleviate your symptoms. Lowering the temperature may also help.