First of all, you are having heart related problems and come on a message board asking for advice? Any problems to do with your heart, you should go speak with your doctor first and foremost. Nobody here knows your medical history, and you don't want to take any chances.
Secondly, heart problems are not a known side effect of using Finasteride. That being said, there are some studies out there that indicate it MIGHT cause heart irregularities. This would probably be in extremely rare cases if at all, and it's probably safe to say that finasteride isn't causing your problems. I would say, judging from your description, that you are experiencing anxiety. Are you? If so, this would be a scapegoat for your problems. Especially if you focus on your heart beat, you feel it more strongly and the building anxiety through worry can make it even worse.
My brother is currently going through the same thing, but he has never touched propecia. He notices his heart beating fast, feels his pulse, sits there and focuses on it, worrying more and more. His heart beats faster and harder, and he's even gone to the emergency room a few times because of it. Doctors say he's just having a panic attack. You didn't mention anxiety so I’m not sure if this is what's happening in your case, but it very well may be.
Good luck. Again: SEE A DOCTOR!