A 4-year-old child experiencing an elbow injury while playing, with symptoms of crying, refusal to let anyone touch the elbow, and keeping the elbow extended, is typically indicative of a specific condition. Among the provided options, the characteristics of this scenario most closely match that of a "pulled elbow." Also known as "nursemaid's elbow," this condition often occurs in young children when there is a sudden pull on the forearm. The mechanism often involves the radial head slipping out of the annular ligament, commonly seen in incidents where a child's arm is pulled suddenly while extended. This results in pain and reluctance to move the elbow, similar to the situation described. Other conditions like radial head fracture, supracondylar fracture, or elbow dislocation would likely involve different mechanisms of injury and presentations such as visible deformities or swelling, which are not mentioned in this scenario.