Hello, I'm another one for the stiff neck gang (but not from running)!
The best thing you can probably do is go to a Chiropractor! It may be that your spine is misaligned somwehere and this is causing your neck problem.
As far as exercises go - I have been advised against using the rowing machine so you should probably use it with caution. Make sure you don't have any problems with your back that may be aggravated before commencing specific exercises.
Oh, and an ice pack would be better than heat - it reduces inflamation and helps manage pain.