Even with ideal pH of 7.5 (see this link) and no chloramines, your eyes are going to get irritated if you keep them open in water that isn't high in TDS. Human tears have around 9000 ppm so a standard pool with 500-1500 ppm is likely going to give you a problem. Even saltwater chlorine generator (SWCG) pools with 3000 ppm salt will still cause pressure and swelling in the eye, though it will take longer. One would need to get near 7000 ppm TDS before one eliminates the problem (see this paper).

The problem is due to osmotic pressure since the water in the pool is more concentrated than in your eye (the extra salt in your bodily fluids makes the water less concentrated) so water enters into your eye until the pressure in the eye builds up to equal this osmotic pressure. Over time, this pressure irritates the eye. Note that this issue has nothing to do with chlorine -- having your eyes under pure water would cause the same problem, probably even faster.

Richard