Hello and welcome to HCM.
Yes,the degenerated cervical disc can give rise to such symptom.
If I were your treating doctor,I would recommend
-Antiinflammatory tablets like
ibuprofen or naproxen for couple of days
-Applying cold compress over the area for 20 min for 3 times a day
--follow some muscle relaxation exercises for neck and shoulder
-temporary support like brace to the neck
-if still pain persists,muscle relaxants like baclofen can be given under physician's prescription.
Also blood pressure measurement, ECG,blood glucose and
blood lipids tests are required to evaluate medical conditions like
diabetes mellitus,
atherosclerosis,
heart disease.
-avoid smoking and excess alcohol intake.
Just would like to ask you whether this pain is over one or both the shoulder?
You can revisit again for any further query.
Thanks.