How horrid! Your poor friend must be so distressed about this mess!
It sounds like the burn is down at her nerves so I don't know if any of these suggestions will work.
Lavender Essential Oil and Apple Cider Vinegar have both worked for me IMMEDIATELY after I have burned myself with oil -- with no aftereffects. I think that the Aloe Vera plant is supposed to work as well. This is from memory, but I believe that Jason Winters (who now manufactures and sells herbal teas) used honey to heal his face after chemo/radiation (?) on his cancer-ridden jaw. The docs told him not to tell the other patients what he was doing -- too cheap and it worked.
Since the burn is no longer on the surface, I am not so sure that any of the above (except the urine?) could work -- our son had been on the lake for hours on one brilliantly sunny day -- no shirt and he got one stinking burn. I put nothing on it that day, but three days later, he was in terrible pain and would run and jump into the bathtub for relief (we kept the water in the tub so that he could get immediate relief). Nothing that I put on him at that time did any good - I was too late. Just getting cool in the tub was his only relief for a couple of days.
After I read a story of a boy's burns being healed after using some old urine, I decided to keep a jar of my own (three years old now).
I hope that MH can suggest something that is effective.