It sounds like your son may have a supracondylar humerus fracture, a fracture of the bone right by the elbow. When this bone breaks, there can be damage done to the arteries that pass by the elbow, the brachial artery. The artery brings fresh, oxygenated blood from the heart to the body tissues to provide nutrients. If the artery is damaged, the amount of blood flow is compromised and damage can occur to the cells that are starving for nutrition.
One way to tell is if your son had a pulse at the wrist. If he didn’t, and his hand was cool to touch, he could have this type of damage. On the other hand, he could have a pink, warm hand but still no pulse – this has a high chance of still having damage to the artery. If the doctor knows there is damage, surgery must be done as soon as possible to prevent that further damage.