If it's just your arm going numb and nothing else is happening then you most likely are not having a heart attack.
Arm numbness can be a sign of a heart attack but if you're having a heart attack not only your arm will be numb but other symptoms you should experience are chest pain, lightheadedness, pressure on your chest, palpitations, shortness of breath and fatigue are some major symptoms that go along with a heart attack.
Your arm being numb could mean that you just lost some blood flow to the area and your arm has gone to sleep.
If the numbness in your arm has gone away after awhile then it was most likely just loss of blood flow to the area in your arm.
You could also have a damaged nerve in the arm that is numb and should go see a doctor if the numbness persists or doesn't go away.