The best first aid treatment for such is to immobilize the body and particularly the affected part especially in the absence of ice that can be placed over the closed wound as was Aron's case. The reason for immobilizing the part and the body is to reduce the internal bleeding. This is exactly what he did, he calmed himself down and tried to avoid movements at the initial time when his arm was crushed. After the amputation, he ended up with an open wound that was prone to further bleeding and even infection. To avoid such from happening, the wound was adequately covered with the available clothing.

Aron also ended up with crashed bones on his right arm after breaking free from the grip of the rock. This meant he was to travel with he fracture over a distance. To reduce the pain and further damage to the fracture, the appropriate first aid was a makeshift sling that he used to firmly fasten and secure his arm against his chest to reduce the movement of the arm.

Aron also...

The first aid skill that he used to handle this in the short-term was to elevate it above the heart as is recommended. This elevation ensures there is minimum swelling of the sprain. Aron used the sling to achieve this.
Strains also occurred with Aron on his muscles fibers or tendons. The recommended handling of such is also close to how sprains are handled and he bandaged the strains, applied the elevation on his right arm that had suffered the strains at the wrist and protected it to prevent further infections in the course of his search for medical attention.

During the night hours when it became extremely cold, Aron learnt to keep himself warm through wrapping the climbing ropes that he had around his legs since he was in short pants, he also used the earphones to keep his ears warm in a bid to avoid hypothermia.