Antacid seems not suitable to my case, since I don't feel sour at the back of throat. For your father's case, do you find on what main source cause sour taste at the back of throat?
We never got to the bottom of it, but he feels it was due to gastric acids flowing into his pharynx. He never used antacids, but I'm making this suggestion for you just to see how you react to it. He felt the sourness when he coughed very hard, so it wasn't always present.
1) Check any bacteria or virus causing Tonsils or Throat inflammation
If you had a bacteria infection in the stomach, you'd feel the pain physically. Similarly, throat infections are easy to distinguish, they normally subside within a week. Sometimes throat infections lead to tonsil stones that are lodged into it; this happens when white blood cells are sent to an area of infection, they leave microscopic calcifications behind that, over time, may lead to tonsil stones.
2) Check throat inflammation caused by stomach acid
a) Eating too fast
b) Helicobacter pylori
c) Other
(a) Unlikely
(b) Unlikely
(c) Yes
A doctor should be able to provide you with better advice because they know your medical history, your physical condition and perform blood tests if required. Please update us when you hear from your doctor.