There are a few different possibilities here, and I suggest that you go see your primary care doctor
about the issue, especially if the spots worsen or persist. They will be able to examine your nose and help you figure out what is going on.
One possibility is that these are "pimples", especially if they are reddened and raised with a white point. Pimples often occur inside the nose, because there are several types of bacteria that can live in the nose and cause them.
If, on the other hand, the white areas are more diffuse and not rounded or pimple-like, then it is possible that this is simply inflammation of the nasal mucosa from, for example, allergic rhinitis (nasal allergies). When the lining of the nasal passages becomes chronically inflamed, this often gives the tissue a pale white appearance which might be what you are seeing.
Both pimples inside the nose as well as swelling of the nasal passages from allergies or chronic irritation are conditions that can be easily treated. Start by seeing your primary care doctor, who can formally confirm a diagnosis and, based on their findings, help you decide what kind of treatment might be in order.