I get the same kind of beats you are talking about. I get the hard thumps which can take your breath away and I get the flutters that last a few seconds. On my holter is showed as PVCs and PACs. I think it is pretty common.
If this is a new sensation though, I recommend talking to your heart doctor as they may want to do a holter just to verify what it is you are feeling. It may not be heart related at all but just anxiety. If that is the case, you will know your heart is strong and find reassurance in that.
Good luck :)
Lots of people get extra beats, skipped beats, fluttery feelings and it is usually nothing to worry about. The extra beats are called ectopic beats and they originate either in the atria or the ventricle of your heart. Sometimes these extra beats cause you to feel like your heart skipped a beat or a flutter in your chest. But the only way you can be sure what is going on is to have them caught on an EKG or a Holter monitor. Since you are experiencing chest pain, dizziness, shortness of breath and fatigue along with the heart palpitations I would strongly encourage you to go to your doctor and have things checked out.