Hi Marilyn @marilyncarkner, I'm not aware of any connections with burning and itching in the upper arms with PMR and GCA. It's not uncommon to have multiple autoimmune conditions along with the PMR/GCA. The symptoms you describe, sound a lot like Brachioradial Pruritus.
--- Brachioradial Pruritus: https://www.ncbi.nlm.nih.gov/books/NBK459321/.

Did your rheumatologist offer any suggestions as to the cause or what may help with the burning and itching?