Your psychiatrist is right. You can give yourself symptoms for every disease known to man through the power of your brain alone. I have had heart failure, brain tumours, blood clots, POTS, Aortic dissection etc etc. Of course I haven;t had any of these illnesses, I have just had the symptoms that were created by my anxiety.
Keep up the work with your psychiatrist, eventually you will believe that it is panic and anxiety and that your kidneys are working just fine.It is horrible to go through but it does take time and you will get over this.
Good luck
It does sound like panic to me because I don't think you could tell if your kidneys stopped working momentarily. What would that feel like?