I doubt that all you describe is caused by the same thing. The "…sharp pains in my to part of my lungs,…" could be musculoskeletal from bone or muscle, neuritis from inflamed or compressed nerves, especially the intercostal nerves that run at the bottom edge of the ribs and encircle one's chest, or simply "shooting pains" that are sharp, often severe, "electricity-like" pains that can occur in any part of the body and usually last from a few to 30 seconds or more. These pains are seldom an indication of serious disease and, to the extent possible, should be ignored.
The most common cause of "…shortness of breath, tightning of my chest,…" in a young or middle-aged person, able to run 3 miles, would be exercise-induced asthma, the symptoms often occurring shortly after exercise, rather than during the exercise. Heart burn/indigestion is often a sign of acid reflux from the stomach, which can occur at rest or with exercise, and is often associated with asthma.
The most worrisome causes of chest pain, shortness of breath and tightening of the chest would be disease of the blood vessels of the heart, also known as coronary artery disease (CAD), and blood clots to the lungs, also known as pulmonary emboli (PE). Your description is not highly suggestive of either of these, but you would do well to discuss your symptoms with your doctor who might want to do some testing to rule-out these more serious causes.
I wouldn't rule out GERD either, can mimic a lot of things and if you reflux into your larynx can cause sore throat and problems with lungs, believe me, been there done that.