There is no documented evidence that one CAT scan can cause such damage to the salivary glands. It is possible that she was fasting for a long time before the CAT scan which may have induced this problem. Sometimes, after injection of contrast (dye) during the CAT scan, some patients experience dryness of mouth, shortness of breath
, etc. which may have been exaggerated in your friend. However, this is temporary and settles within few minutes. Her symptoms are probably unrelated to the scan.
She probably will recover her existing salivary function soon. As for Sjogren's a definite diagnosis needs to be made before she can be treated and an expert consultation maybe required.