I cut the side of my mouth such that the skin inside is flapping. what should i do?

Probably nothing.: Unless you have a huge oral laceration we tend not to stitch up lacerations in the mouth because of the significant increase in sense of infection. The mouth is a really really dirty place. If you think the laceration is very large and then you should go to the emergency room and have it stitched but make sure you get covered with antibiotics.