Wife has rash behind left ear and has spread down neck. Neck rash is bumpy but didn't start that way behind ear. Bacitracin hasn't helped?

Rash. Consider lyme,eczema, staph,which will not respond to bacitracin.Go to urgent care/doctor for treatment.
Contact allergy? Does the rash itch? If so, this may be from an allergic reaction to something like hair products. Since the earlobes are not involved, it is unlikely to be nickel allergy. But if it does not itch, then it may be from something else. If it itches, try hydrocortisone cream and change hair products. If the problem persists, see a dermatologist or allergist. If no pus or pain, infection unlikely.