What is wrong when you have shoulder pain that feels like an electrical charge running down your arm?

Nerve problem. Sounds like you have a pinched or compressed nerve. See an orthopedist or neurologist. Often times the longer youy wait to be treated, the worse the condition can get.
Pinched nerve. Your problem sounds like it could be a pinched nerve. But it the pain radiates down the left arm, a heart condition could be involved. Depending on the severity and longevity, see a doctor asap.