stomach related (bare with me)

Your throat works like this - its a muscle pushing food down into your digestive system. Similar to how a ziptie works, what goes through can not go back. You throw up when the muscle opens up on purpose to get rid of something your body believes is bad for you. Same at the opening to the stomach there are flaps like doors that opens one way but not the other way (again unless throwing up). And acid isn't always in the stomach, its released only when there is food dropped in from the esophagus.
Sometimes acid does escape a bit, it splashes and causes heart burn, acid reflux, and there is a disease where it gets bad (GERD).

It doesnt flow through our throats for a number of reasons, first of all you oesophagus is composed of muscle that expands and contracts to get food down to your stomach, this stops anything flowing back out right away, the part where your oesophagus connects to your stomach is called the esophageal sphincter, it acts like a valve ( doorway ) that opens and closes only when food is entering your system. So when you're not eating, it remains shut and keeps the acid in :) . And the reason why its not allowed to flow through the throat and out is because, unlike your stomach, your throat doesnt have a layer of mucus that protects you from the digestive enzymes and acid in your stomach so, thats why vomiting burns. You digest your own digestive track :P