You have a problem with your pulse, it is true, but not the problem you think it is: A constant pulse of 60 would be a sign that you are inactive, and that your heart is not getting the exercise it needs to stay healthy. The heart is a muscle, and must be exercised vigorously to remain strong throughout life. The only way you know that your heart is being exercised adequately is by getting your pulse rate up to 2/3 of the desired maximum for your age, and sustaining that rate for 20 minutes or more 2 or 3 times per week. I do not know your age, but you can find out the estimated maximum for your age from a doctor, or in a medical book about the heart. For example, when I was a 50 year old doctor my maximum pulse was 180, and so I exercised to get it up to 120-130 by running and racewalking for a few miles, for about 30 minutes, in order to strengthen my heart. Now, with age, my maximum pulse is down to 140, as I am 71 years of age and in perfect health. Two hours ago I walked rapidly for two miles, to keep my pulse well over 100 for 35 minutes.
Sixty is only the right rate for a heart at REST. Whenever you are doing anything but resting it should go up, in proportion to the intensity of your activity.
I hope that this corrects your seriously WRONG notions about pulse. If it does not point you in the direction of vigorous exercise in order to raise your pulse to keep your heart strong, then you must consult a psychiatrist or psychologist for treatment of your ERRONEOUS, IRRATIONAL fear.