There is a problem called whiplash associated disorder (WAD). Patients with this problem experience neck pain, stiffness, and tenderness over the neck muscles. Sometimes there is a decrease in neck and/or shoulder motion.
Compensatory patterns of movement as you describe are not uncommon after a musculoskeletal injury. Pain can lead to a change in the way muscles contract and relax. They lose their natural rhythm and timing when they hold tightly to avoid painful movements.
This is a phenomenon called reflexive inhibition. Other muscles change the way they function to help compensate for the inhibited muscles. Sometimes there is a protective response as muscles contract to hold the arm in a position that reduces pressure on irritated or damaged nerves.
Any of these motor impairments can become “stuck” creating an ongoing feedback loop that doesn’t stop when the injury is healed. It’s not usually something you can change or control easily without some outside help.
Physical therapists are able to examine movement patterns, identify impairments, and help restore normal function once again. Some therapists who specialize in human movement impairments use biofeedback units that help them analyze specific motor patterns. You may want to seek some help with this problem before it becomes a chronic (long-term) situation with other negative side effects.