You want to be as gentle as possible so try to avoid the sore spots. A medicated cream or ointment can give relief quickly. Try to keep the irritated area as clean and dry as possible.
Keep the area around your nose moisturizzed. You can apply vaseline to the area to keep it moisturized or neosporin for open sores. Use a soft gentle kleenex.
The skin irritated under the nose from blowing nose should be treated simply by applying a moisturizer. This can be in the form of a lotion or ointment.