Yes, when adding the last part is to emphasize, but they mean the same thing. "A mí" would be the whole formula, but in regular spanish it's not used because then you can already say it with less words. Have a nice dau!

Hi Iee, Let me show you an example of using “a mi” for emphasize in a sentence ¡Mírame Iee! (Look at me Iee) ¡Mírame a mi, no a el! (Look at me, not him!) Hope this helps

Mírame seria lo correcto, "a mí" está de más pero si lo puedes usar para dar énfasis.