A.B.
I had the SAME problem with my 2 year old daughter, with tons of hair! She's barely starting to 'get over it'. I started putting her in the bathroom while I took a shower, and showed her how I tilt my head back so the water doesn't go in my face. I also started using a wash cloth for her to hold over eyes "just in case" the water rolled down her face. I no longer use a cup to rinse her hair... I've been more successful using an extended shower hose (& my daughter has learned to 'trust' that more).
Brushing her out was also always a battle. I've tried several ways to distract her, and the best one so far is flavored chapstick. She will now sit still for a few minutes, while I spray condition & comb her hair. Good Luck!!