There are a couple of different causes of this kind of burning sensation inside of the nose. The first potential causes, which is particularly common as the weather starts to get colder and the air to get drier, is that the lining of the nasal passages because dried out, leading to burning, cracking, or even nose bleeds. The best way to treat this problem, at least initially, is as you suggested to try using a nasal saline spray (which you can buy in the pharmacy).
The next potential cause is nasal allergies, or allergic rhinitis. This is also quite common, and is typically provoked by a whole assortment if indoor allergens like mites and mold. Often with nasal allergies there is stuffiness or sneezing in addition to the uncomfortable burning sensation. Nasal allergies can be treated with a combination of allergen avoidance and anti allergy medications like anti histamines and nasal steroid sprays.
I would suggest that you start by going to see your primary care doctor
. They will be able to examine inside your nose and help figure out whether this is simple a problem of dryness or if it is related to allergies. Based on what they find, they can recommend the appropriate treatment.