I'd say that it is probably normal.
Think about it, if you can feel your pulse all the way in your wrist, the chances of being able to feel a pulse so much closer to your heart is even more likely.
I'd recomend that you not press on your stomach to check it, it can only fuel your fears, and trigger a panic attack.
A pulse is normal, unless you are dead. Lol.
You'll be fine, friend. Keep your head up.