Hi, Susie,
I have had dark circles literally all of my life...imagine baby pictures with dark circles...yuk...
I have multiple causes: sinus swelling, facial structure, allergies and bad sleep habits.
The post above is right on: see if the shadow disappears when you press down on the higher skin area. Are you chronically sniffly/stuffed up? Are your orbital (eye) sockets sort of large relative to your eyes?
I have given up on cremes and just take care of my sinuses and use a good concealer/highlighter on the low spots. Also, it never hurts to be careful about rubbing or pulling on that thin skin below the eye. I hope this helps some,
Nelle