Thanks for the information.
I think there are two likely possibilities other than tendonitis for your symptoms.
I would be concerned about the possibility of either labrum injury with a possible nerve impingement in the shoulder, or a pinched nerve in the neck.
The labrum is a structure in the shoulder made of cartilage. Sometimes it can be damaged by trauma or "wear and tear" without any specific injury. If it is injured, sometimes it will also cause a nerve to be pinched as it runs through the shoulder and this can result in pain or less commonly numbness down the arm. This can usualy be diagnosed with an MRI of the shoulder and may respond to steroid injections and physical therapy. If not, sometimes surgery is needed to correct the problem.
The second possibility would be a pinched nerve (specifically the "C5" level nerve root) in the neck. This can be due to arthritis or a bulging disk in the neck. The neck pain and numbness you are having make me suspicious this is a strong possibility. This also can be treated physical therapy as well as pain medications and sometimes injections around the nerve root. However, surgery also may be needed if symptoms persist.
Since your doctor has examined you and suspected a shoulder tendonitis, I suspect that you have or had some tenderness in the shoulder. For this reason, it may be best to start with a re-examination of the shoulder and to have an MRI of the shoulder. If the MRI is normal, you may request an MRI of the neck to look for a pinched nerve there.
If your doctor is not comfortable doing this, an Orthopedic Surgeon would be the best type of doctor for you to see in my opinion.