It was about this time after my radiation that I stopped wearing a bra for a while. If I was going somewhere where it make me uncomfortable, I had a large back brace I would hook around me instead. I know it sound weird but they did not move or rub and it had a soft material inside.
Oh and I think I used a gallon of 100% aloe (no alcohol) I kept it in the fridge and put it on whenever I got uncomfortable. This period blessedly did not last terribly long. My heart goes out to you right now, I can remember the misery of it, all these years later.
Is it cool enough where you live to put on an oversized soft cotton and just go braless? Have you talked to your doctor about that new gel patch that is supposed to help the burn?