Demodectic mange is usually seen in small dogs, less than 2 years old, because their immune system is weak. And as far as I know, humans rarely get infected by this infestation. But as you are saying that you and your pet are facing skin irritation, itchiness and rashes then there are chances some parasite has surely affected. You can try topical treatments like powders, shampoos, dips made for treating mites. There are oral medications and injections available on the market that you can give a try. More than anything, make sure your dog’s living environment is clean because if that is not taken care of, mites will easily reside and all your efforts go waste. BTW happy national dog day! Lots of love to your buddy..