On Saturday I vomited 3 times after drinking a lot of alcohol it has been three days now and my throat/back of my mouth still hurts how do I stop this?

Will stop on its own. From vomiting, either alcohol or stomach acid caused damage to the back of your mouth/throat. Allow for time to heal. It should resolve in 1 week or so. Avoid spicy foods, alcohol until fully healed. If it doesn't heal, see your General Practitioner.