1. Seems you are suffering from Left sided brachialgia or thoracic outlet syndrome
2. Do you have neck pain
too? Does the symptoms aggravate on one particular position of your neck or arm? If yes then it is advisable to go for a Xray of your Cervical spine
3. Thoracic outlet syndrome needs a proper examination by an orthopaedician
4. Building shoulder and neck muscles can reduce such symptoms.
5. If not improving its better to undergo MRI
of your Cervical spine and left shoulder to find out exact cause and proceed.
6. You might need orthopaedic, neurosurgeon +/- neurophysician consultation.