I Just Discovered My Roomates Dog Was Recently Diagnosed With

I just discovered my roomates dog was recently diagnosed with mange. It's quite excessive as she is old. Just as recently I've developed a red, scaly, bumpy and itchy type of rash going up my left arm onto my back left shoulder. Could I have mange from the dog/could the mites that caused her mange cause me to get scabbies? Or is this just some sort of rash or eczema? Also, how should I treat this? Thank you.

-Madelyn