We don't have the shortage for healthcare workers here that many parts of the country have. However, outside of Charlotte itself (smaller towns) there may be more openings.
That doesn't mean that there would not be openings for a CST.
The two main hospitals here are Presbyterian (Novant) and Carolinas Medical Center (Carolinas Healthcare System)
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Just check out job openings on these websites. That is where I would start.
Good luck!