Regardless of how you draw, you will eventually become muscularly imbalanced. Muscles develop a thing called tonus, that is they will hold themselves tight. If your neck muscles didn't do this, your head would flop around out of control, when you least expect it. As was said, it is equally possible to artificially cramp up your neck with bad head positions. It is also very possible that you could be aggravating a dislocation. A good chiropractor can get you back to a neutral location, but you have to do things yourself to keep your muscular balance to maintain a stable neck. first thing to do is to make sure that you are not cramming your neck when you draw. Your neck does not draw your bow and you should not need to torque the crap out of it to find a good anchor point.
When I get going for the year, I shoot anywhere from 300 to 500 arrows a day, I know too many. I shoot two to three hours in the morning and then again later in the day. I put up to 18 arrows in my quiver. I shoot both left handed and right handed every day, I also do a variety of exercises with dumbbells with an adjustable weight bench. Not for draw strength, but for muscular front to back balance, this helps keep the shoulders centered and the arms balanced. I need to ride bike more for cardio, but I have a serious case of the winter lazies going.