Shortness of breath, heartburn, cough that won't go away, chest X-ray and EKG are normal? What could it be?

Bronchitis . Is a viral disease characterized by prolonged, excessive, dry coughing. He most common symptom of acute bronchitis is a cough that is dry. Acute bronchitis is a one-time condition that lasts for several weeks. Drink plenty of fluids and otc medication. Rec. See your pcp if symptoms persist another week.
GERD. Gastro esophageal reflux disease. Avoid smoking or caffeinated beverages after 5 pm (and avoid late night snacks ). May help to take Pepcid (famotidine) daily.
Allergy/GIT. Could be allergy to some foods or meds. Or some git problems like indigestion or hyperacidity.