If you could help me by answering a few questions it will help me get a better idea of what may be going on.
How old is the cat?
What breed and color?
Is he/she an inside outside or both?
How long has this been going on?
Is the sore flat or raised and red?
Is where on the nose is it located?
If a sore is not healing there has to be an underlying cause. In the case of light colored cats who have been outside there is an increased occurrence of skin cancer. This usually appears on the tips of the ears or the nose.
As the scab heals it becomes hard and itchy. This is why she is knocking it off. You can try aloe vera gel. This will help with the healing and keep the tissues that is needed for healing soft. A good deal of the aloe will be absorbed into the tissue. If she licks it off it will not hurt her. There is also Aloe juice that is suppose to boost the health of the tissue form the inside out.
I do not know wither your cat has a problem with inadvertent self mutilation or if it is skin cancer. Try the aloe if it dose not heal even with a soft scab she will need to be checked for the skin cancer.
I hope this information has helped.