It really depends on how far you want to move your head to the left -- going too far causes pain because its a warning against damaging your neck.
Nerves that provide sensation to the arm come out of the neck.
If a normal range of motion is causing pain, I imagine that you have something not quite right on the left side of your spine.
You'd be wise to consult with a doctor to see what's going on in there, as it probably won't get better by itself.
Many people have that symptom. It is something to get checked out by a medical professional (make an appointment with your doc, or go to an urgent care center). It could be something as simple as a temporary pinched nerved (needing nothing more than an ice pack), or, you could have a spinal nerve-impingement issue, or, it could be something else more serious.
The sooner you find out what is going on, the sooner you can be doing stuff to make it better! :-)