The part that was injured with the sliver has developed inflammation as a natural body response and he may also be having superadded infection in the area. He needs to take a course of antibiotics and pain killers. The hand should rest in a sling and not allowed to hang down as this will increase the swelling as well as the pain. If antibiotics are taken on time if symptoms will resolve otherwise abscess
may form and you may have to consult a surgeon to drain out the pus.