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

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.