What is the treatment of persistent itchy throat.

It is not treated. Itchy throat and ears are merely signs of some illness or infection. So after a exam and possible tests, the actual cause is determined, and then treatment would be given.

If you are in the US, specifically in the north and the east to middle part, you are probably suffering from allergies. I don't even have allergies that I know of and am itching, coughing, and a bit congested, for weeks now, especially after mowing the lawn. One of the worst springs ever.

See if an OTC anti-histamine works first. That's what any doctor would say.
Pollen is tiny spiky balls that actually do get stuck in the throat and nose. Your ears are connected to your throat.