I cannot give you a clinical diagnosis over the internet unfortunately and my opinion cannot substitute for a formal medical opinion
While your symptoms may be more likely to be due to muscle or
tendonTendon repair strainStrains , a pinched nerve in the meck at the C5 root level can cause pain that radiated in to the shoulder or upper back. If more severe it ca also cause muscle wasting and weakness of lifting your arm from your side.
This can be evaluated by the neurological exmination. If there is pain only and signs of musckulosketeal injury, you may not need any furhter neurological testing. If there is suspicion for a pinched nerve, an MRI of the cervical spine or an EMG needle study can diagnose this. Surgery is usually reserved for progressive neurological disability or intractable pain, conservative treatment such as rest! is usually reccomended.
Good luck
A pinched nerve does not seem the most likely explanation based on your informtaion, but is possible. If a nerve is pinched in the neck, the pain typically radiates past the elbow and is usually accompanied by hand/arm tingling and/or weakness in a specific muscles of the arm or hand which correspond to the spinal nerves being compressed or pinched. It is less likely that a peripheral nerve in the area of the shoulder is being compressed.
It sounds like you may be having some type of shoulder problem, especially if you do not have any neck pain.
The only way to sort out these possibilities is to have a thorough examination including, but not limited to your neck, shoulder and a thorough neurological exam. A primary care physician/internist, chiropractor or neurologist should all be able to sort out these diagnostic possibilities. In some circumstances, advanced imaging such as a MRI or electrodiagnostic may ne needed to get a specific diagnosis.
The treatment will be determined by the diagnosis. Depending on the diagnosis, conservative treatment by a chiropractor or physical therapist may be beneficial for your condition. Surgery is always a last resort since this is the most invasive and radical type of treatment.