Hi Charly, bless you for trying to sort this out for your lovely friend. It must be hard for you to stand by and see her in pain. All I can suggest is some Bach's rescue remedy cream, gently rubbed into her hands and then some cotton gloves over if she can tolerate it. I know that my dad pulled away when I tried to hold his hand due to his treatment, so he must have been sore too. He had radiotherapy though but it probably leaves the skin feeling similar.
I do feel for you, and for your friend. The thing for her mouth might be Corsodyl mouthwash, depending if she can use that, or salt water rinses or Bonjela or clove oil, but it might be too strong for her. Plus she would have to check all with her nurse or doctor. Plenty of good foods, vitamins are essential, as I am sure you know, if she can tolerate them.
Thinking of you and I hope that she is soon more comfortable and out of some of the discomfort and pain she is in. 