A strain is caused by the over stretching or tearing of muscle fibres. It is usually less serious than a sprain. Do not try to diagnose either a sprain or a strain at home unless the pain is trivial and the child begins using the affected limb after some time, which means all is well.
Comfort the child as the accident must have scared the child. Let him put the limb in whatever position he feels most comfortable in. Do not try to make him use it, he will do it by himself if it is not affected.
Do not try cold compresses and bandages. If it is a fracture, you may make matters worse. And if it is a sprain, your treatment will be of no use because the doctor will have to undo it when you get to the hospital.