Are they sure its in your neck? You could have a impinged shoulder meaning the nerves are pinched either at the suprascapular notch or at the spenoglenoid space. Or it could be pinched under the acromion. Google shoulder impingement, internal impingement and quadrilateral space syndrome.

If its pinched actually in your shoulder and they do a cervical epidural or facet block or nerve root shot it could make it worse because if its pinched in the shoulder it is yanking on thos cervical nerve roots.

Have you had and EMG done? Have they done an MRI of your shoulder?

Using ultrasound to look at the shoulder is a new thing some pysiatrists are doing. Thats how they saw my pinch nerve in the shoulder notch. It was swollen and pinched and irritating my neck. My neck MRI showed only minor damage and its in the shoulder. I had a c6 nerve root block and it totally made things worse.

Hope this helps.