Pain in the shoulder, arm, and scapula as well as pain in the back while bendng the neck forward. ~3 minutes of chest CT scan, normal 2 months ago; smoker; worried about pancoast tumor. Is a repeat chest CT scan necessary?

You need a good Doct. A good doctor should be able to investigate your problems with the relevant tests. You are thinking about rare cancers. If you were a heavy smoker and over 50, then you might think about pancoast tumor but it is unlikely in your case. The pain can come from chest, bones or spinal canal/spinal cord. A good physical exam and closer look at all structures in the area of the pain should help.Diagnosis.
No. If you had a normal ct two longs ago there is absolutely no need to repeat.
Consider MRI. It is hard to say without a detailed exam. But i would think if you had a ct scan of your chest just 3 months ago that was normal, the yield would be pretty low to get a repeat ct scan again looking for a pan coast tumor ( unless there was something wrong with the first one). If you have not had one, consider an MRI of the thoracic and cervical spine to rule out a spinal cause.