Why do I have pain in my upper arm when I touch it or move it?

Shoulder or armpit? Could be an inflamed node or early abscess if armpit involved. If shoulder, would think strain if trauma or lifting involved. If muscle stain heating pad/anti-inflammatory medications, trauma , ie contusion , cold compresses.
? near shoulder. Tendonitis about the shoulder is probably the most common reason the upper arm gets sore to the touch. See your doctor for examination to clarify.