Muscles in the upper arm will limit movement of the shoulder joint as well as the elbow seeing that these muscles run over more than one joint.
Nerves in the upper arm involve a big bundle of power cables running on the inside of the armpit to the inside of the elbow. When they get compressed they produce pins & needles or numbness that spreads into the fingers. Some patients experience neck pain associated with upper arm pain, which leads us to investigate the nerves running out of the neck all the way to the fingers. These patients suffer from a condition called Thoracic Outlet syndrome.
Major arteries run alongside the nerves and can cause bleeding after a fall onto the arm. The famous pain radiating to the left upper arm can be referred pain from the heart, and must be tested during examination.