When I first started getting in shape after being very lazy, I would have bad shortness of breath and a racing heart and other aches and pains. It freaked me out, it seemed abnormal that I would get so winded so quickly, I thought I was irritating my heart/lungs and it was indicative of something more serious. But I kept pushing (even though I felt like I was a ticking time bomb) and my lungs and heart adapted to the new workout program and I was just fine.
I think in order to start the process, you should just dive right in. Let yourself get winded and exhausted the first time, tell yourself it's not going to actually kill you, no matter how bad your heart hurts. Remember the pain will be real because your body is taking a shock, but the anxiety is all in your head, there's nothing wrong with your heart, your heart is racing and reacting as all hearts do when anyone starts getting in shape. After you live through the first experience you will feel more confident doing it the next day and the next and eventually you won't worry about having a heart attack.