Both my kids did that too. Its pretty normal.
They get preferences and fears and just reach a point where they don't like the water running down their face or the soap or just the process of it. And they get scared even.
My son is 3 now, and he still HATES washing his hair. So it takes me AND my Hubby to do it. Or, we use a wet washcloth with a tad little shampoo in it, to rub down his hair and then rinse with a cup... tilting his head so the water runs OFF his face and toward the back. And, we give him a dry washcloth to hold over his face.
OR, we have him lay down on his back, in the tub... and rinse that way. Supporting his neck so that the water level does not cover his face/ears (which he HATES).
Washing hair is just not pleasant for many kids and a torture.
You really do not have to wash their hair everyday. I don't myself. Only when it is oily/dirty. Because otherwise my hair gets dry. Same for a child and their hair. Even our Pediatrician told us that.
Good luck,
Susan