If your child has fallen on to their elbow, it can be dislocated; this means the bone has been dislodged out of place. Your child may be in pain, and the joint may not look normal, or it could move back into place. Your child may experience swelling, and pain when moving their arm.
You should seek medical attention because of the ligaments, tendons, nerves, blood vessels, and muscle in their arm may have been damaged. Or your child could have possibly broken a bone (also known as fracture). 
An elbow injury can be caused often by falling or overstretching the arm. This injury is not common in young children. The risk of an elbow injury is greater when a child becomes more active such as, riding bicycles, roller skating, and sports.
If your child experiences an elbow injury, but the elbow looks normal and shows no signs of pain, or may not want to use their arm ( they will keep their arm close to their body).This could mean that the ligament that crosses the top of the radius bone in their arm may have been displaced or moved. This type of injury is common in children under the age of 5. It is not as severe of an injury such as a dislocation or a fracture, but it is still recommended that your visit your doctor about your child’s injury.
If your child has experienced a dislocate elbow, do not try to reposition the dislocated joint yourself. This can cause more damaged to the surrounding tissues, nerves, and blood vessels. Seek medical attention immediately.