My left jaw has been hurting and my gum is sore around my tooth on that side. What could this be? And how can I stop the pain?

See a professional. See your Dentist who is trained to diagnose the source of your pain (could be tooth or gum infections) and can then provide the best treatment. This is not a DIY project, you need to see someone with the training and experience to examine you and then answer your questions. Call NOW. Delay will only allow the infection to spread.
Infected tooth. or an abcessed tooth. Take otc nsaid and also apply otc oragel to the gum after gargling with and antiseptic oral solution. In the mean time call your dentist.