Hello!
Most wounds that require closure should be stitched, stapled, or closed with a skin adhesives within 6 to 10 hours after the injury. Some wounds that require treatment can be closed as long as 24 hours after the injury, however, the risk of infection increases the longer the wound remains open before closure.
Injuries to the mouth and lips bleed more than injuries to the other areas of the body, but they rarely require stitches. The near constant blood flow to that area also allows the wounds to heal quickly. If the blood will not stop, or you can pinch the edges of the wound together and are able to close the wound doing so, you may require stitches for the mouth wound.
You mentioned that the wound is due to a dog bite, therefore, you may need antibiotics. If the wound displays typical signs of an infection (fluid oozing from the wound, tenderness in a surrounding area, loss of sensation around the bite, swollen lymph nodes, fever, chills, fatigue, or any flu like symptoms), seek the attention of a medical professional for examination.
I hope you feel better soon!