I sleep on my left side and have done since I can remember, for the last few weeks when I try and sleep both my arms start to go numb. It is very uncomfortable and because of this it takes me a long time to fall asleep. When I wake up both my arms are completely numb, the numbness is from my elbows down into my little fingers, the rest of my hands are not affected. I also suffer from lower back pain that no doctor can find a cause for.
It sounds like you are compressing the ulnar nerve at the elbow, called cubital tunnel syndrome. The most common ways this nerve gets compressed is by bending up the elbows or by direct pressure on the insides of the elbow.
Compression of the ulnar nerve at the elbow causes the small finger side (ulnar side) of the forearm and hand, to go to sleep.
If the numbness and tingling does not go away within a minute of so, or you develop it at other times of the day, you may want to see a hand surgeon for an evaluation.