I have a couple of suggestions for you:

Do you use menthol mints, gum or peppermint tea regularly/daily?

If so stop all menthol containing products for at least a month, and see if anything changes. Some people are very intolerant of menthol (peppermint).

Also avoid acidic things for a while too... citrus drinks, fruit, vinegar etc. Sodas contain both citric acid and phosphoric acid, and these may be irritating a nerve in your throat.

Doing an elimination diet like this may reveal your problem.

If you have an irritated nerve, it may be due to a past viral infection. Try some lysine supplements for a couple of weeks and see if that helps. These are inexpensive and have no side effects.

You might want to get a B12 test run to see if you are low. Nerves cannot repair themselves if this nutrient is in short supply.

Have you tried a cold pack on your throat before you eat or drink liquids? Cold would numb a nerve and if it does help it
points to a nerve problem.

If you are taking statins for cholesterol, you might consider discussing with your doctor, getting off of them. They cause nerve damage in some people.