I got that last part backwards...should read "because the injury is lower." In fact, my mind is a little backwards this morning! But hopefully you get the idea.
Well, that burning in your chest might be a lung issue, so you could go to a pulmonologist and have them check out your lung power, see if you have a breathing problem, or perhaps infection in your lungs. That's the next step I think you should take, becuase it sounds a lot like you have a "chest" infection, which means your lungs are compromised by bacteria, for example. But to answer your question, yes, you could have a pinched nerve in your spine, which if it's in your thoracic spine, for example, those nerves come out from the spine and wrap around your chest, and can cause pain.
Find an anatomical picture of your nervous system, and see how the nerves extend out from the spine and what they affect, like the arms or legs or breathing. You know how a person can break their back, and then they can't move from, say, the legs down? This is because they hurt their back in the lumbar region, where the nerves go down from the lower spine into the legs. Likewise, if you get your neck broke, the cervical spine, depending on which vertebrae were affected, it can partially goof up your arms, but miss affecting your breathing because the injury is higher up.