Sorry that pain meds don't work, but in cases where there is spinal cord damage that's the way it is. The pain is not where you feel it. It's coming from your brain which is interpreting every little touch, even from other areas as pain.
It's called central cord syndrome, and it's not fun. Sometimes a big course of prednisone will reduce the swelling and help, but if it goes on then that's the way it may stay. I crushed 6 vertebrae and broke off a bone spur, which crushed my cord at C3-4, in a fall on my head. Sometimes the pain problem is called central pain syndrome. http://centralpainsyndromefoundation.com/
After a few weeks or months you may get spasticity and possibly big clonic spasms/jerks. You also have to watch out for the symptoms of autonomic dysreflexia, which can be fatal if not treated immediately. Look up the terms!
The swallowing and talking is because the surgeon shoved the trachea out of the way in order to the surgery. I had particular trouble with that because of being post-polio and not swallowing well to begin with. I had a naso-gastric tube for feeding for a couple of months.
Hopefully your problem will not be this severe. I would ask the doctors if a course of prednisone might help.