For me the doctor screw up my neck and caused cervical radiculopathy, took them years and years to figure it out, MRI wasn't invented until I was 12, and when that came to our hospital in a semi trailer as it was considered the (portable MRI). They found it immediately. The tech who was actually taking the pictures. Exclaimed "Oh, my god!" And I think called in the whole hospital.
Now I can do push-ups, planks, etc, right along with Cathe, now. The only thing is say I do CoreMax, my hands have to be behind my head for all the ab exercises done on the back. It's just not possible for me, to climb the rope and have my arms out in front, I can do two ore three reps and then my hands have got to support my head.
But if I were you, I wouldn't be doing any of it. Not even step, as that jarring of stepping up and down, can cause a lot of little damage that the doctor will chew you about. If you have to have surgery that first time you step up and down a stair case in physical therapy, you'll think you just jumped off a 10 foot step and onto the ground with the way your neck muscles react.
Running can jar it as well. I don't know how bad yours is. Mine was pretty extreme, but sit down and rest, you'll be in much better shape and won't cause any problems when they look at your neck. As the worse thing you can do right now is aggregate it and make the problem look worse then it already is.
I know it's aggregating, and it's hard to sit there and not workout. But really it's better then aggregating the situation. I'll be praying for you, that it's not too bad, and it's a real easy fix, with out much pain. And you'll be good as new in no time.
Kit