HELLO AND WELCOME,
the tearing of gums/gum split is common during extraction of tooth.
usually the socket area heals by its own ie,by primary intention.
please do approximate the gums with your fingers to enhance healing.i would also advice you to take warm saline and betadine
rinse to remove the infection os socket.
take the antibiotic course prescribed by your dentist
if it do not heal even after a month please do visit your dentist.
avoid chewing food in that area.
please do not hurt the area using needle/toothpick/stick etc.