Does tendonitis in the arm go away and why are surrounding muscles, breast, neck, and back aching?

Activity causes it. Look at the activity that you are doing that causes the strain on the tendon. Stop what you are doing or figure a different way to do it. The other pains are from you guarding the part that hurts and moving abnormally. Sports medicine research shows that the most effective treatment of acute tendonitis is a big ice bag and an ace wrap. Not 2 tight! it aches 6 minutes before it gets numb.
Slow to heal. Tendonitis and strain, sprains and tears of muscles are notoriously slow healing. Sometimes the injury occurs from issues with posture or overuse or strenuous activities that can be causing the pain in surrounding areas. Sometimes, the strain comes when trying to protect or compensate for the injury. Please see your family physician for an evaluation and physical therapy may be indicated.