First of all I am very sorry to hear that your son burned his arm. This is a very good question. However it is one that I am unable to answer thoroughly without more information from you (or your son pending his age), and without being able to examine him thoroughly. Thus I am happy to give you some general information, but would recommend that you see a physician for an exam, and perhaps more importantly they will take a thorough personal history.
First of all burns in general can be caused by heat, electricity, chemicals, friction, light, or radiation. The etiology of your sons burn is important in determining treatment. Classification of different burns can be quite diverse, but in general there are three main approaches: classifications by depth, classification by severity, and classification by surface area. To best answer your question about sensation, I will focus on the "depth" classification system. This is the system that most people are relatively familiar with and it refers to the "degree" of the burn. (i.e. first degree, second, third and fourth). First degree burns involve the most superficial layer of the skin called the epidermis, they look red, are dry, and are painful. Second degree burns extend through the epidermis into the dermis, are painful, moist, and blister.
Third degree burns extend down through the entire dermis, are painless (since the nerves are burned), and are usually dry and leathery. Fourth degree burns extend through the epidermis, dermis, sub-cutaneous tissues, and into the muscle and bone. Thus if the burn was a third degree or worse (which I doubt unless it was a catastrophic burn), the feeling should still be intact. I would recommend seeing a physician (primary care physician
) to go through your son's history with you. Hope this helps.