Shooting pain down the arm with numbness suggests a nerve problem.
Possible causes include a pinched or compressed nerve in the neck or in branches of nerves that travel through the shoulder or arm. Arthritis in the neck or a bulging ("slipped") disc can also be the cause.
Another possibility is a muscle strain or tear. A muscle injury may cause swelling that irritates a nearby nerve, causing numbness. Shoulder injuries commonly cause pain that is felt in the upper arm rather than in the shoulder itself. This phenomenon is called referred pain.
Other causes of pain after exercise include tendonitis, a stress fracture, or a joint injury, but these are less likely to cause pain that radiates from the shoulder to the fingertips.
If your symptoms continue, see your doctor for an evaluation, as there are many possible causes and treatments for your symptoms.
Find out more about this book:Harvard Medical School Low Back Pain: Healing your aching back