I wouldn't wear a brace, without supervision by a PT.

If you wear a brace, for any length of time, the muscles in your neck will atrophy. When you take it off, you will not be able to support your neck properly, which could aggravate you symptoms greatly and reduce your range of motion.

Wearing a collar, for short periods, can provide relief for those with unstable necks. However, that needs to be accompanied by a regime of isometric exercises to avoid muscle wastage. In the end, the ideal is to deal with the problem, not just mask the symptoms.

When one first injures the neck, the swelling actually provides stabilization. As it abates, muscle atrophy can allow too much movement and create symptoms, like headache. This phenomenon is why many patients feel that they are regressing and why rehab is important. In most cases, gentle exercise can rebuild the muscle and stabilize the situation.

Have your neck evaluated properly by a competent professional. The best course of treatment could range from surgical stabilization with rods to strengthening exercises.

Hang in there.