Does a cervical herniated disk cause horrible shoulder pain?

It can. Severe shoulder pain is a common symptom seen in cervical disc herniations. There can be further radiation of pain down the arm as well.
Yes. A cervical disc herniation can definitely cause severe shoulder pain and pain that runs down the arm into the hand. It is not the only cause, however, and so a detailed physical exam can usually determine the cause followed by appropriate studies such as an mri. Thank you for the question.
Yes. This can be a part of the presentation of a cervical disc herniation with or without neck pain as well as with or without arm pain or neurologic symptoms or findings with pain over the shoulder or along the inner border of the scapula or shoulderblade being a common site for pain due to a disc herniation.
Yes. Specificaaly, classica lly the c5 nerve root is the neck suspect causes severe shoulder painf oud betwern c45 a dic herniation at that level can cause severe shoulder pain.