It's pretty common to be aware of your own heartbeat. It's not unusual. The reason you sometimes don't even notice it is because your brain chooses to ignore it, just like it ignores your nose making you not being able to see it anywhere else than reflections.
Im almost constantly aware of my heartbeat but that's due to my heart arrhythmia (most certainly not due to caffeine, I tend to stay away from that) as well as anxiety. But it's never been said by any doctor to me that it's unnatural for me to feel it