I am having left upper arm pain on the side just below shoulder. it's a small area, maybe 2 inch circle, that feels like bad bruise but no discoloration and no known injury/trauma. there is no radiating pain. it is very sensitive to touch?

That is a common area where people bump themselves and do not notice or remember it - when walking through a doorway, getting out of a car and lots of other typical daily activities. The bruise may be in deep and so you do not see the color. Take Tylenol as needed and apply heat to help heal and for comfort. See a doctor if not signficantly better in 4-5 days.