How do I cope when my job forces me to turn people away?

You are good at the work, steady and reliable at securing a crossing through whatever comes. But the job puts you at a hard seam, between the duty you are sworn to and the human stories of the people you have to turn away. Carrying both at once is a real and heavy thing. That tension you feel is not a malfunction. It is your conscience still working, and you should be glad it does, because the day turning people away costs you nothing is the day something in you has gone cold. You can do your duty and still feel the weight of it. Those are not in conflict. Holding both is what it means to do a hard job as a full human being. What you cannot do is carry every story alone in silence. Find a way to set some of it down, talk with others who face the same seam, or simply let yourself grieve the calls that deserve grieving. You did not write the rules you enforce. Do the job with care, feel what there is to feel, and do not let it harden you.