Elbow pain for a week that radiates to the shoulder and arm. also to the back. feels like pinching? feels better with rest

Can be pinched nerve: Pinched nerve when it passes in a groove in the back of the elbow can cause it. This can be from inflammation, scarring, or bone spur. Occasionally Carpal Tunnel syndrome will cause the same. If rest, by avoiding activities that cause pain, and icing does not take care of it in few days, then you need to see your primary doctor for further evaluation, testing, and treatment.