I have had really bad back pain (right side under shoulder blade), accompanied by cough. Could this just be muscle strain from the cough?

Only one way. to find out: go see a healthcare provider who will examine you properly and tell you whether you need further tests to rule out any potentially lethal causes including blood clot (pulmonary embolism), tumor/cancer, obstruction, nerve compression, or simple muscle pull. Thanks for trusting in HealthTap.