Look for hypoallergenic shampoo, if you can't find any at your local horse supply store you can look for hypoallergenic baby/human shampoos as well. Good luck!
I would go to a tack shop and look for hypoallergenic shampoo. I know the colour enhancing stuff is really bad for the horses.
He can’t use any type of shampoo
What type of allergies does your horse have? Grass? Hay? Pollen?