There's no harm in hearing your own heartbeat just like there's no harm in hearing other things.
I like to hear my heartbeat every once in awhile using a stethoscope and it's a good way to detect if anything might be going wrong with your heart.
If you get to know the sound of your heartbeat and then the sound becomes different later on when listening to your heartbeat then you know something may be wrong and you should see a doctor about it just to be safe.
So if you want to use a stethoscope to check your own heartbeat you sure can without any problem.