Extreme pain in the gum behind my last left molar?

You have a wisdom tooth trying to come in. You need to see your dentist. He will x-ray the area and determine if the wisdom tooth is impacted or just trying to erupt. Either way you will need to have it removed. Wisdom teeth serve no purpose and are routinely removed usually under general anesthesia. You won't feel anything. But take care of it before it causes you any more trouble.