It is very important not to rub, massage, shake, or apply physical force to the cold burn tissues in an attempt to rewarm it, since it can be very harmful and is not recommended.
The area need to be rewarmed by immersing the injured arm in a water-bath that is held just above body temperature.
Anti-inflammatory drugs like ibuprofen are recommended for pain control and reduction of the inflammatory process.
Antibiotics, taken orally can prevent infection to occur.
It is best, this cold burn to be evaluated once more by her physician, since some dameges develop after the first day of injury.
Only, her physician can determine the degree of skin damage and the appropriate treatment.

Best wishes!