What is the best method to relieve constant muscle pain/tightness under the shoulder blade curving to the side under my arms?

Exercise. Muscle go into spasm for several reasons. An imbalance of chemistries: sodium, potassium, magnesium...Or dehydration are two possibilities. Most often, though, is a lack of active use: contracting and relaxing the muscles to coordinate them to work properly and maintain a natural state of muscle tone. Get started on a regular exercise ad strengthening program and eat more fruits and vegetables.
Muscular tension. Most of the causes of pain in the back of the chest is muscular in the setting of poor posture, scoliosis, osteoporosis or other. A kyphotic spine is one that bends forward. Stand up against a wall with your back of head resting against the wall. Your shoulder blades too should feel the wall.
Danger here. Rule out danger first, like a pleural lesion on your lung. See your doc. It could also be a tendon tear, or muscle pain seen in patients who never sleep deeply. Relief depends on cause, a good diagnostician, see one.