As you dont appear to have a lung problem, breathlessness while lying on your back could indicate a heart valve problem or high blood pressure. If your blood pressure is normal lying on your back, then it is probably a valve problem.
A floppy Mitral heart valve can be without major symptoms in the early stages and breathlessness lying down,varying with body position could be an early symptom. Anxiety states can also cause increased adrenaline which can affect the mitral valve.
A lot of MVP problems can be due to low magnesium and can be alleviated with a high absorbable magnesium supplement. Try it for a couple of months, if no improvement see your doctor.