89 yr old with right side of back itching, is it anxiety?

Itching one side bac. Best bet is to examine the pt. Make sure there is no scabies or skin disorder, urticaria or something else.
BACK ITCH. How long has this been going on? From your description, is sounds like it may be a condition known as notalgia paresthetica. Also called brachioradial pruritus. Have you had an injury to your neck before this began? Change your laundry detergent to all free & clear. Use an otc Hydrocortisone cream twice daily. See a dermatologist for this common disorder if it doesn't disappear.