helpless89,
You are compressing some of the peripheral nerves in your upper extremities, by the position you place them in when sleeping.
You have brought the elbow up into a tightly flexed position. This can cause the ulnar nerve, behind the elbow, to be compressed in the cubital tunnel. This would cause the small and ring fingers to go numb and tingly.
You may also be compressing the median nerve in the wrist, by laying your head on your hands. The median nerve is compressed at the base of the palm. This would cause numbness and tingling in the thumb, index and middle fingers.
You might try sleeping with your hands, not under your pillow.
If however, the numbness and tingling continues, despite the change in position, you may want to see a hand surgeon for an evaluation.
There are other places where the nerves could be compressed.
Good luck.