Had chest ct scan 3 months ago and was clear. now i still have chest and back pain and shortness of breath. can it be lung cancer even after clear ct?

Yes, but not likely: Unlikely in your age group anyway, but especially with normal ct. Nonetheless, almost anything is essentially possible. I would be more concerned about blood clots or other conditions with those symptoms. Either way- stop smoking!

Probably not.: Why did you have a ct scan 3 months ago? In a 35 y/o with a clean ct scan, lung cancer is very unlikely. There are many possible causes of chest pain and shortness of breath, which would require seeing a doctor for an exam and testing to determine the likely answer.