Hearttransplant patient, suffering from very bad cold, cough, now shortness of breath to the point, of being scared to lay down?

Call . Call your transplant coordinator! you are at risk and need complete advice.
Short of breath. This may be from the upper respiratory infection, but probably a good idea to call your cardiologist and get checked out. It could easily be pneumonia or bronchitis. However, if you start coughing up yellow or greenish sputum, then get seen by someone soon.