The answer is NO, you should not try to adjust your own neck. The cervical spine is a delicate area that houses nerves, ligaments, joints, blood vessels and your spinal cord. This is not an area that you should be messing with because you will most likely just be making the problem worse.
If you need adjusted, please go see a chiropractor and don't risk seriously injuring yourself. A chiropractor will be able to identify if there is a greater problem at the source of your neck pain and work to correct it in a safe way.