This may be due to a thyroid problem which your vet can check for with a blood test.
Skin infection and irritation is one common symptom of that. The bad body odor can be due to yeast or staph growing on the skin due to the thyroid issue. You can read about thyroid issues here
http://www.marvistavet.com/html/body_hypothyroidism.html
Another possibility is an autoimmune disease such as lupus or pemphigus which you can read about here
http://www.upei.ca/cidd/Diseases/immune%20disorders/pemphigus.htm http://www.upei.ca/cidd/Diseases/immune%20disorders/lupus%20erythematosus.htm These autoimmune diseases have several variations in how they present.
I'd plan a vet check up for her to start working on the problem.
In the meantime to protect the nose you can try some plain petroleum jelly on it for the cracking.
Hope this helps you!
Dog Expert:Rescue, Train,Breed,Care
30+ yrs dog home vet care & nursing, rescue, behavior&training, responsible show breeding, genetics