Why does my dog have a black rash on her arms and stomach?

she is a five year old pure breed pug and she has had if for about a year and when we took her to the vets, they said it was just skin sensitivity and gave us dog shampoo to use to get rid of it. it hasn’t been working and her rash is getting worse. the rash on her arms is raised, and is black and scabby looking and the skin around it is red and irritated. and on her stomach there are black spots that look like the start of it again. shes always chewing on her arms, so I’m guessing it is very uncomfortable for her.

Do you know what this is? or have any experience with this? any help would be appreciated(: