What can cause new musculoskeletal, non-cardiac chest pain and l. arm and underarm nerve tingling in healthy subjects? recommended tests?

Nerve pain: Irritation of the brachial plexus (the nerves that come together and then branch to go to the arm) can cause these symptoms. Overuse, carrying a backpack, trauma are common causes. Less common are inflammation of the nerves or compression of the nerves. I'd recommend starting with a nerve conduction study (EMG) and then further testing would be based on those results.