Hello~Yes, a pinched nerve in your lower neck can cause chest pain. The burning is usually a sign of a pinched nerve. I would see a chiropractor, he/she will take some x-rays of your neck,look them over and then discuss the results with you. After a few treatments, these feelings you are having should be better.
Also, yes, anxiety can cause chest pain and tightness, but, with the symptoms you have, it still sounds more like a pinched nerve caused by a vertebral subluxation (meaning neck muscles and vertebrae out of alignment that need attention.)
3 years is a really long time to suffer anything! My husband also will say he has chest pain. As he has heart disease in his family, he's also had about a gazillion tests. For him, anxiety. That is the final diagnosis. He takes Zoloft and it helps. He still will tell me has occasional chest pain but he is checked annually with nothing showing up. He does have high cholesterol which is completely controlled with medication.
Have you ever looked into anxiety?