What could cause shooting pains that seem to come from elbow to shoulder and back in my left arm?

Your neck. Thank you for the question. There are many potential causes, but among the most common is the irritation of a nerve in the neck. The term "cervical radiculopathy" refers to the pain that can run don the arm into the neck from a nerve irritation in the neck. Uusally a phyxical exam and appropraite imaging studies can diagnose the problem.

Related Questions

I've been having shooting pain down the back of my left arm between the shoulder and my elbow?

Pain. Make sure there is not a pinched nerve in the neck with proper physical exam and possible MRI and/or nerve conduction test. Read more...
See your Dr. You need to be evaluated by your doctor. You will likely need an MRI of the cervical spine. Good luck. Read more...