Such a rash on nose can be due to seborrheic dermatitis. Seborrheic dermatitis is a common skin condition that causes flaky,dry, white to yellowish scales to form on oily areas esp under the nose or anywhere on face. You can treat flaking and dryness with over-the-counter dandruff or medicated creams which contain salicylic acid, coal tar, zinc, resorcin, ketoconazole, or selenium.
The other possibility is of atopic dermatitis for which I suggest you to get it evaluated from a doctor.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing