Scared I have lung cancer. I quit smoking after 4 years, having shortness of breath & back pain doctor not worried after a clear chest X-ray. Chances?

Rest assured. It is good you quit. It is good your results satisfied your doctor. There are other causes of shortness of breath and back pain including GAD, which you have. Take this opportunity to try some CBT therapy. It will teach skills in mgmt of anxiety and build confidence in your good choices. It is not atall likely that you have lung cancer or that you will. Think about it.
Lung Cancer Scare. At age 32, even with a significant smoking history, it is unlikely that you have lung cancer, especially with a negative chest x-ray. The shortness of breath ("dyspnea") needs to be evaluated by a pulmonologist, however. You could have something as common as asthma to account for the dyspnea, but it needs to be evaluated soon.