Often injuries to the rotator cuff muscles in the shoulder will refer pain to the upper arm, or even down the arm. If your shoulder and upper arm pain is aggravated by lifting, reaching overhead, and sleeping, that sounds like an irritation or inflammation of the rotator cuff.
The rotator cuff is a group of muscles that surrounds the shoulder joint, and while they are often injured during a specific traumatic event, you can also develop rotator cuff pain without an obvious aggravating activity. If there is associated weakness, then I would become more concerned about an actual tear of the rotator cuff tendon.
Constant pain, even at rest, or symptoms that include burning or numbness going down the arm, would make me concerned about the neck or cervical spine. Occasionally nerve irritation at the neck can mimic a shoulder injury.
Initial treatment consists of rest, ice, and an over-the-counter anti-inflammatory medication (Ibuprofen or Naproxyn). Many times, the pain and irritation will then go away. If symptoms persist, you should be evaluated by a shoulder specialist, to make sure there is not a more serious injury.