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There could be several things going on. It takes about 7-10 days for antibiotics to completely clear a bacterial throat infection. Viral infections aren't affected by antibiotics so they aren't prescribed for viruses. Post-nasal drip can continue to cause sore throat for some time. With a red esophagus, you may also have some acid reflux (GERD) which is stomach acid that comes back up the esophagus to the throat. Often sore throat is the first symptom before someone actually experiences any heartburn. Another possibility is a condition called globus hystericus which is the "feeling" that something is in the throat when there really isn't. It is a form of anxiety.
Any time you have an upper respiratory infection, you are subject to having pain in your head and eyes. Fluid causes it. Of course it will get better over time. You've only been on antibiotics for a few days, and if it is bacterial they haven't had time to act yet. If it is viral, you can count on feeling under the weather for about 2 weeks. If the redness in the esophagus is reflux your doctor will probably prescribe 2-3 weeks of an acid reducer like Zantac or Prilosec to see if that makes you feel better. Globus hystericus is treated by treating the underlying anxiety either with cognitive behavioral therapy or medication or both.