Hello, Welcome to Just Answer and thanks for your question. Has your doctor checked you for GERD? This is gastroesophageal reflux disease in which stomach acid refluxes back up through the esophagus into the throat and can cause pain. That is a far more likely scenario than a throat infection spreading to the esophagus. Acids in the digestive tract are able to take care of simple things like strep and most common sore throat viruses. That isn't to say that you may not have an infected throat as well. The culture will determine that for sure. Many antibiotics can cause stomach distress, so be sure to take yours with food.
Your throat really doesn't sound like strep. Strep makes your throat look like raw hamburger and hurts really, really bad. Rash isn't all that common with it though. Penicillin usually clears it up in 4-7 days. No throat infection should be causing esophageal discomfort though.