It sounds like your dog may have seborrhea oleosa. You can read about it here:
seborrhea Canine Seborrhea
I have seen this in dogs before and it can be hereditary or it could have been caused by other things, like over vaccination. You might want to ask your vet but until then I would bathe her in a medicated shampoo and rinse her in apple cider vinegar.
The Wonders of Apple Cider Vinegar
I am so happy you rescued this little girl. I wish you the best of luck with her. Please keep us posted on how she is doing.