Answer:
amygdala
Explanation:
Based on the information provided within the question it can be said that the part of the brain most likely damaged would be the amygdala. This is the part of the brain that is responsible for emotions, survival instincts, and memory. Therefore if you are not afraid of certain situations, animals, or events it is because your survival instincts for those situations are not working properly, therefore there is something wrong with the amygdala.
Best way to put is is, Survival of the Fittest.
Applying ice to a fire victim leads to tissue hypoxia and necrosis because it will change the skin's temperature too fast and may cause frostbite. The burn could have had removed a layer of skin, leaving the fragile tissue exposed which will be more sensitive to the ice.