What are common causes of a sharp pain that shoots down the back of your leg?

Muscle or nerve. For a young person, the most likely issue is muscle pain in the 'posterior chain" these are the muscles that keep you erect. These include the buttocks and the hamstrings as well as the low back muscles. They could be responding to a problem in the lower back.. Or you could have an si, sacroiliac, issue. You could also have a pinched nerve from a herniation of the lumbar disk in the low back.