I think you should see one of the CCF neurologists while you are at your checkup, call the neurology appointment line to set one up - 216 4445559, ask for a neuromuscular section neurologist
pain and pins/needles in the arm in that distribution can be from irriation of the C6 nerve root. Usually this is from compression of the nerve root by a bony spur, as you may actually have. Brachial plexus injury is a possibility but rare, the difference may be apparent by examination and by the needle EMG study. TOS is a rare diagnosis and is probably unlikely.
Exacerbation by swallowing is unusual, but may possible be due to something pressing on the esophogus while swallowing (bony spurs/degenerative neck disease can do this, or possible by regenerating nerves sending signals the wrong way.
See if your CCF doctor can set up an EMG study of the left arm while you are here also.
Good luck