I am sorry that your nose has been feeling chapped. You should follow up with your primary care physician
to ensure there are no other symptoms or workup required for your condition.
Your are likely correct that your nostrils are red and painful from excessive nose blowing. This is a common finding that can occur during colds or during winter months when more people experience rhinorrhea (runny nose). Vaseline is a great way to protect your nose from further damage and to help with the sensation of dryness and pain. Vaseline especially is good for this because it does not have extra fragrances or chemicals that can by drying or irritating to skin. Also, vaseline is thicker than most lotions and creams and does better at retaining moisture and forming a protective barrier over the skin. You should also try to use soft tissues to blow your nose rather than rougher paper towels or napkins. Additionally, using a humidifier at home can also help prevent excessive skin changes by preventing a dry environment which can lead to overall dry skin. This is especially helpful during dry, cold winter months.
Red, painful nostrils can be due to increased nose blowing during a cold, but you should still follow up with your primary care physician to make sure no further testing is required for your symptoms and physical exam findings.