Although jogging burns more calories than brisk walking, within the same time period, you have to modify the exercise according to your own body requirements.
If you would like to continue jogging then take these precautions:
Wear a cushioned pair of shoes when you jog so as to reduce the wear and tear of the joints
Jog on a soft surface like a mud track or a field instead of hard ground or the floor. This will again ensure less wear and tear.
If you are overweight, in the long run, you might just be increasing your risk of getting joint problems, not only in your neck but anywhere in your knees, back, shoulders etc.
So you might like to alternate jogging with brisk walking or any other aerobic exercise to get the same benefits without the risks.