Laying on my left side pain starts in my right palm moves up to my elbow should i be worried?

Hard to say: Is your hand and arm fully functional and the pain minimal? This sort of complaint might prompt a nerve conduction test to see if you have a trapped nerve that might need surgery

Probably not: This is likely the result of nerve compression or pressing on a nerve. Even though you are not lying directly on the nerve in the palm, part of the nerve fibers that affect the palm are being compressed by your body weight when you are lying in this position. I presume it goes away when you change position. It doesn't do permanent damage, but avoid that position if you want to avoid the pain.