Most dogs like to scratch their backs because it's an area that they can't reach easily so it could be she's just getting older and has some extra aches and pains. It's also possible that she has/had a bug or tick on her back that was itching her.
If your dogs got tangled up and that triggered the behavior it's possible she has a nagging injury and is seeking relief by rubbing against different objects. See how she responds to your touch on her back, see if you feel anything unusual and if the behavior persists you could consult with your veterinarian. They might be able to recommend something over the phone and save you a visit (and a bill) if you call them at the beginning of the day before they get busy.
If your dog isn't eating you can try baiting her food with some warm broth. Chicken or beef stock is inexpensive and you can heat it until warm in a pan with some water and then drizzle it over her kibble. This will often entice your dog to eat everything and lick the bowl clean. A few days of eating regular may help her get back to normal. Good luck!