Can this tear in my earlobe heal by itself since it did not split all the way? (Photos)

Hi,
This is a common problem. Whether it is from trauma or over time from heavy earrings, the piercings can stretch. Unfortunately, they typically do not heal on their own. In my practice, we repair these under local anesthesia using a z-plasty to close the opening and re-pierce the ear. 
Mehdi Sina, MD

Thank you for your question.  The hole on the ear is unlikely to heal on its own.  You would need the small hole to be removed and then sutured so the skin can heal back together.  This is a minor procedure, taking 30 minutes, performed under local anaesthetic.  All The Best