Not trying to scare you but...
The symptoms you describe could all be due to a sleep disorder, such as obstructive sleep apnea. You should discuss this with your primary physician (PP) and ask if a formal sleep study is warranted.
However, another explanation for daily shortness of breath and cough COULD be a pulmonary emboli. It is very easy to screen for this condition with a lung scan or a CT of the lungs, programmed to focus on clots. Also as Mega said a cardiac ultrasound would check the valves, function and size of the heart.