What is the best way to cure a dry nose without getting a major acne breakout?

Non-comedogenic crm. If your nose is dry and flaking, then use a non-comedogenic moisturizer designed specifically for the face. However, often what people believe to be "dry" skin on and around the nose is in fact "oily" scale from a different condition called seborrheic dermatitis. Try some head & shoulders shampoo as a face wash a couple times a week and see if the flaking resolves. Otherwise, see your doctor.