A hernia in your neck will not heal on its own, ever. The disc resides between the bones is known as intervertebral fibrocartilage. There is not a source of blood flow that go into the disc. Without a blood flow there is no way to get for the disc to get nutrients to heal on its own. The pain you feel is from the nearby nerve being pinched, usually down an arm. The situation is exaggerated because of inflammation in the area. The doctor is trying to bring down the swelling in an attempt to relax the pressure on the nerve. As long as the disc is not directly touching the nerve, this is a very good help. I went through this for quite some time, give the shot a try. If it does not help there are other options. I would not worry about the interaction between the Prednisone shot and any test you are taking. The chances of an adverse side effect are small and if you don't get the inflammation under control it will continue to get worse.

On a side note I had a C6-C7 herniation and went through it all. Eventually I had to have a disc replacement (Bryan Disc) and its been great. Lifting heavy does not help.