I was in a car accident a year ago. My neck has been bothering me for about 4-5 months. Could it be because of the accident?

No. A car accident from a year ago would have resulted in symptoms almost immediately or within a few days, not over 6 months later. You should see your physician for further work up.
Yes. If you haven't had any treatment yet, x-rays would be appropriate since it was a traumatic event. Assuming that was done and clear, a course of physical therapy, anti-inflammatories, and possibly a muscle relaxer should help for myofascial pain, which is fairly common in these cases. If those don't work, a neck MRI would give more information.
Yes it could be. Car accident could cause neck injury or could agrrivate already minor problem in the neck?