lol people have good suggestions, but that's just it. they don't work. lol. Give him his own shampoo would work if you cold get him to stop panicking, lol. Been there!
well, I tried it all too and my daughter went through a phase that lasted a year, from about that age. Nothing could calm her down (and please trust me when I say tearless shampoos are not all tearless. When in the eyes bad enough they can be irritating. we discovered that the hard way). My advice is this: switch to the kitchen sink if you can, make it quick and limit the number of hair washing you do a week down to 1, unless he really needs it. get him to hold a cloth over his eyes for rinsing (or you do for him).
what got my daughter to stop her fear was actually our new baby. When the baby started having sink baths at around age 5 months or so my daughter saw how much the baby loved it and started calming down herself. that's actually how we graduated her into a big tub, too. She was terrified of the water draining out so we put the baby in, (who loved it) and she was so jeallous the baby was playing in bubbles that she leaped in herself! lol
It was be one of those things "this too shall pass" at some point! hand in there. Like I said, ours was a full on year!