Neck pain that travels down the arm can be caused by several problems. Angina and heart attacks can sometimes present this way — especially on the left side. But arthritis with bone spurs, disc herniations, and even postural issues (head forward and shoulders slumped) can create similar symptoms.
In the case of nerve compression, irritation, or impingement, the neck pain going down the arm is referred to as cervical radiculopathy. A change in neck and arm position (such as wearing a neck collar) can shift the structures that are pressing on the nerve enough to alleviate the pain.
You might get the same effect by standing up straighter and lifting your shoulders slightly. In fact, if wearing a collar and/or changing your position relieves your symptoms, then you might be a good candidate for chiropractic and/or physical therapy care.
Stretching tight muscles, correcting posture, and realigning the joints is a more permanent solution to the problem than wearing a neck brace. Sometimes there are muscle imbalances that need to be addressed as well. Usually a short series of appointments with a home program of stretching, postural exercises, and strengthening may provide a permanent solution to your problem.