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The good news is that you had a CT scan that was negative. This suggests the problem is not coming from an enlarged thyroid or a mass in your neck pressing against your esophagus. Unfortunately, you are still having the discomfort. It is very likely that this is the tail end of a viral infection, which doesn't necessarily show up in you bloodwork. It can cause a sore throat and lymph gland enlargement, all while not being affected by the antibiotics (they only treat bacterial infections).
It may simply take another week or 2 for your body to clear the virus. Another possibility is a chronic sinusitis, which is often missed as the cause of a chronic sore throat. The CT scan likely didn't include your sinuses, but is an excellent idea if your complaint continues. These infections can require 21 days or more of antibiotics. Also, your sinuses drain while lying in bed at night, which would explain your worsened symptoms in the morning.
If this is all explored and negative, I'd recommend getting an endoscopy so someone can actually visualize your esophagus and rule out any inflammation or ulcer that can be missed on CT scan.
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