What if your heart feels like it is vibrating from time to time for 2 days and you sometimes cough due to the vibration?

Palpitations. By vibrating, you probably mean sudden onset of rapid heart rate which starts and stops suddenly, it can cause shortness of breath and cough, it should be checked out by your pcp / cardiologist. It needs work up including lab / holter monitor / electrocardiograph, etc. See your md asap.