Can muscle tightness cause shooting pain? non cardiac shooting chest pain sometimes goes downwards into my stomach. some in upper back as well.

Back trauma?: Shooting pain is often neuropathic pain, which is often associated with a secondary muscle spasm. (cardiac or noncardiac is open until the diagnosis is established!) neuropathic upper back and chest pain does happen (i.e., in thoracic nerve roots disease, aka radiculopathy), although it is not very common. If any history of back trauma, MRI of the thoracic spine may identify the cause.