They're horrible aren't they?
There are some excellent books by Dr Claire Weekes about anxiety. They're quite old and a bit dated in the style of writing but she covers many of the fears anxiety sufferers have. I'll post below what she says about palpitations/heart worries.
Hope it helps
PALPITATIONS
This short attack of alarmingly quickly beating heart may come, and so often does, just as you are going off to sleep, or may even wake you from sleep. Do not sit up in panic. The more you panic, the more adrenalin is released by your glands and nerves and the quicker your heart beats. Although you may think, "Ah, I wish the doctor could feel my pulse now! My heart really is racing!" I still suspect that if you take your own pulse you will find that its rate is not much more than one hundred and twenty beats to each minute. Even if it is, it is not important. A healthy heart can tolerate a rate of over two hundred beats per minute for many hours, even days, without evidence of damage.
HOW THICK AND POWERFUL IS YOUR HEART MUSCLE
Also, you may think you can feel your heart beating in your throat and are sure it will burst at any moment. I can assure you it will not. The full, bursting feeling is no more than the unusually hard pumping of the main arteries in your neck. Your heart is nowhere near your throat. If you could see how thick and appreciate how powerful your heart muscle is, you would lose all fear of its bursting or being damaged by the palpitations. I must remind you that I am assuming that your doctor has examined your heart and has told you that your trouble is "nerves."
So relax to the best of your ability (see How to Relax chapter 20) and let your heart race until it chooses to slow down, remembering that it is a good heart, merely temporarily overstimulated, and that such stimulation will not harm it and will soon cease. Should the attack be prolonged, does it matter so much? When you understand the palpitations, are they so terrible? If necessary you can ease yourself by talking to someone or getting up and drinking a glass of milk. Walking about will not harm your heart even though it is palpitating. If you prefer to stay in bed, by all means do so, but lie there as relaxed as possible and let your heart race wtihout shrinking from it. If you do this, one of these you nights you will surprise yourself by dropping off to sleep in the middle of an attack.
As acceptance calms your nerves, the attacks will be less frequent until they no longer come. Many years ago when studying under strain, I occasionally had palpitations. I have not had an attack since. Can you see how foolish it would have been had I become agitated by them? My heart has served me well during the ensuing thirty years.
SLOWLY BEATING HEART
It may be that instead of beating too quickly, your heart occasionally beats too slowly for comfort and you have attacks of faintness, when you are sure it is about to stop altogether. In such an attack you may feel paralyzed, unable to move. This is called a vasovagal attack and is brought on by overstimulation of the parasympathetic nerve, the vagus. You will remember tha the parasympathetic nerves hold the adrenalin-releasing nerves in check. In these attacks they check too severly and the heart slows to an uncomfortable rate. Vasovagal attacks are rarer than palpitiations, but they are just as disturbing if you do not understand them. Remember, the attack is also the result of too much nervous stimulations. Your heart is not diseased. the attack does not harm your heart. As you worry lesss, sustained tension lessens and the attacks gradually leave you. Even after apparent recovery, you may occasionally have one. Do not be disconcerted by this. With understanding and acceptance they seem less formidable. Actually your doctor can prescribe tablets to control them so consult him if necessary. It is well to terminate an attack quickly, as it can be exhausting altough not actually harmful. Although I teach facing and accepting, I do not advocate stoical forbearance,
MISSED HEARTBEATS
A nervously tired heart, a heart stimulated by too much alcohol, nicotine, caffeine, irritated by indigestion will sometimes "miss" beats. The sufferer describes it as "missing" beats, although no beat is actually missed. The heartbeats are merely spaced unevenly. The patient feels as if his heart turns over and a tickling sensation catches him in the throat. He may cough and stand still, wondering what will happen next. "Missed" beats are in no way dangerous, and your heart will not stop because of them. They are annoying but that is all. Exercise abolishes them. So do not let "missed" beats frighten you into lying on the couch again. Most people over forty have "missed" beats now and then. Many young people have them. They are not important.