Hello and thanks for trusting me to help you. I am a board certified consultant with over 30 years of experience.
I understand your concern.
Well as you describe,possible causes of such pain may include Cervical spondylosis/stenosis-nerve compression in it's path due to osteophytes formation from degenerative arthritic changes,bulged disc in neck.
You should see an Orthopedist or Neurologist for a clinical examination and undergo X-ray/MRI of cervical spine and shoulder joint.
As you had already tried anti-inflammatory medications with little relief so your doctor may prescribe opioid pain killers,steroid injections for pain management.
Physical therapy can be tried.
Warm compresses with a heating pad on affected area and back of neck.
And make an appointment with doctor.
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