How would a wound like this heal?

Well it would probably take months to heal at best, it should be treated with some sort of disinfectant, then have some sort of gauze or bandage put over it. There would certainly be nerve damage so your character would not likely be able to feel much with that arm, and certainly not with the part that was wounded. If the skin and muscle don't heal over the whole thing then the bone would be showing making the area extremely sensitive to damage. Meaning she may have to have her forearm cut off from the elbow

if a doctor gives her medication, then i think that will work.

depending on what services are avaliable, the wound could be cauterised- don;t know how to spell it, but applying flame would help to stop the bleeding, ans stitches would probably be used first, sorry dont know the other bit, but long life issues obviously they cannot use their arm, and they can suffer from ghost limb pain, basically they will feel pain or sense touch in an area, even thought the limb has been lost, as the nerves are still active