Left shoulder and arm pain with numbness in hand and fingers and can't raise arm above shoulder?

Nerve root injury: One of the more common causes of your symptoms is a cervical nerve root injury called cervical radiculopathy. In a man of your age the cause is more likely to be osteoarthritis affecting the foramen (hole where the nerve root exits). The reports of numbness argues against an intrinsic shoulder problem and without antecedent trauma a brachial plexus lesion is unlikely. Please go see your doc.

Varies : The most common cause would probably be a pinched nerve in your neck. Other potential causes could potentially include thoracic outlet syndrome or one of multiple peripheral nerve entrapment syndromes such as carpal tunnel syndrome. I would not hesitate to be seen and a good exam could go a long way in determining the cause.

Intrinsic shoulder : Joint problem, such as rotator cuff tear or frozen shoulder joint may be present. The numbness could be indeed "shoulder hand syndrome" or maybe brachial plexus issue associated with the shoulder pain. Perhaps a parsonage turner syndrome or even a thoracic outlet syndrome if symptoms worsen on arm elevation. However, sounds like a mix of joint and plexus. See orthopedic surgeon first.

Shoulder vs. TOS: Reduced range of motion plus shoulder pain and hand numbness are symptoms seen with brachial plexus compression in either the thoracic outlet or pectoralis minor areas. It could also be two diagnoses: shoulder tendonitis or inflammation plus brachial plexus compression. The next step should be a history and physical exam by a doctor familiar with both these conditions.