That thing that hangs down in the back of your throat is called the Uvula. Like any tissue, it can get inflamed or infected and swell. This photo shows uvula edema. (or if you are a Brit it is called uvular oedma)
This patient was hospitalized for acute pancreatitis and developed difficulty swallowing and a sore throat. He had been vomiting repeatedly and that may have been the cause of the swelling. Other causes are infection, inhalation injury, an adverse medication effect or allergy.
The treatment is antibiotics if infection is suspected and corticosteroids to reduce the swelling. This patient's symptoms resolved without treatment.
(Case from Consultantlive)