Maybe. A chest ct scan without dye/contrast injection should only take less than a minute on a newer ct scanner. If you can close your eyes and hold a deep breath for about 40 seconds, and not panic, then you may not need any anxiety meds. You can practice this at home by covering up under your bedsheets at night. The vast majority of my ct scan patients can do their scans without anxiety meds.
Most likely. Let your doc know of your anxiety before the study; (s)he will probably prescribe something like ativan/xanax/valium to relax you during the study. It's important for you to be relaxed since movement produces poor images. Make sure your doc knows all the meds you're taking to prevent drug interactions.