Itching in the nose, together with an increase in the amount of nasal mucus, are both signs that you have some inflammation inside they nose. There are at least two common causes of this.
The first would be a common viral infection, such as the common cold. This may begin with itching and increased mucus in the early days of the infection prior to progressing to a full blown cold with nasal congestion, cough, and other symptoms.
The second common cause would be nasal allergies, which are commonly causes this time of year by indoor allergens like mold, mites, and the like. In addition to itching and nasal mucus, there may also be frequent sneezing, nasal congestion, or eye itching or redness.
I suggest that you go see your primary care doctor
about this issue. They will be able to examine you and figure out what is going on. If this ends up just being a viral infection, then there is no need to use any specific treatment, as it will get better on its own. However, if this is nasal allergies, it will be helpful to take an anti allergy medication, such as an anti histamine, and your doctor can recommend a good one for you.