You are half right. Improper pH level — either high or low — is another couse of eye irritation.
Liquid chlorine raises the pH, but Trichlor, the tablets used more often than liquid chlorine, lower it, as does Dichlor (pool shock).
A strategy I used when I had a pool was to use Trichlor as my everyday sanitizer, and shock the pool once a week with liquid chlorine. I never had to add muriatic acid.
That’s exactly what i do. But I never had an eye issue from the chlorine level.