Hi Cheryl, CT scan uses X-Rays (much higher exposure than your standard Chest X-Ray) and presents higher radiation risks and that too when you have been treated heavily using IMRT. Frequent CT scan is not advisable just for nothing (as your doctor said, you may have or may not have)!

Nothing to be upset about. Even if you want to check your chest, get X-Ray. It may not have too much resolution but it does serve the purpose.

Refer to comparisons of effective radiation dose here: http://www.radiologyinfo.org/en/safety/index.cfm?pg=sfty_xray#part5

For my dad, both his RO and SO have always recommended Head-Neck MRI over CT (since he does not have any other medical condition prohibiting MRI) and for chest he has had 3 X-Rays in last 3 years. They also tend to avoid PET scan as much as possible primarily due to the fact that PET is usually in combination with CT and Radio-isotope use and ofcourse the cost - even though we are ready to bear it but they do not want to overburden us.

Even with low risk for normal patients, it presents significant risk to cancer patients in remission.