Why is the lining of my nose always sore?

Probably from trauma. The inside of the nose is very sensitive to irritation and inflammation. Unfortunately once it's irritated and inflamed we tend to pick it and irritate it further. This can cause superficial infections inside the nose. Get some Bacitracin ointment from your pharmacy and with a clean finger rub it inside your nose four times a day for several days. If this does not help see a nose doctor.
Infection or Allergy. A sore nasal lining may be the result of inflammation due to infection or allergy. Your primary provider or otolaryngologist should be able to check for associated symptoms, perform cultures or nasal lining biopsy and begin appropriate treatment as needed.