10 minutes is better (for the general public) -- we don't want someone leaving an ice pack on and getting the oh-not-so-fun Frostbite :-)
I have this as well and the only thing that works is ice 20 min. on my neck every 3 hrs it will at least ease the headaches and take the sourness out of my neck.
I had the same exact experience and when the medical profession gave up on me, I got to work on fixing myself. It took a month of weightlifting work with a trainer, and it hurt like Hades the first couple of weeks, but the pain and numbness were gone and haven't come back in 10 years. I felt like I had to take the chance of possibly disabling myself - maybe then the idiot doctors would listen! - or fixing myself. Thankfully, it worked. Physical therapy just didn't do enough in the muscle strengthening department to do me any good. My own attitude didn't help in PT at all either. "I can't do that exercise - it huuuuurrrrts!" Guess it boiled down to No Pain, No Gain.
You might want to consult with Dr. John Sarno at the Rusk Institute for rehabilitative medicine in NYC.
You may want to read his book first on TMS syndrome.
He and his colleagues have helped thousands of patieints where "idiopathic"pain was involved.
Good Luck