The next time you have a bath try putting your face in the water and opening your eyes under the water. You will notice your eyes will react to the warm water and if you keep putting them in the water long enough they will become sore, not burnt but sore. During my competitive career from 1960 - 1968 I did all my training without goggles, not by choice but because there weren't any racing goggles at the time. If you wanted to protect your eyes you needed to wear a full-face mask similar to the ones you wear when you go snorkelling or SCUBA diving. During the swimming season (1st of September to Easter) we always trained without goggles and I can tell you there is a very big difference between gritty eyes which seem to have had natural lubricants washed out of them because of the warm water and stinging eyes from excess exposure to chlorine. There was a daily ritual that would happen at school around 11.00 am which consisted of my yawning (tired from swimming training and getting bored during class) and the resulting tears from the yawn would trigger the sore eyes and within moments the tears would be streaming down my cheek as the moisture in my eyes triggered a reaction with any residual chlorine crystals that remained in my eyes. This was embarrassing at first until my school mates realised what was causing it and became a little more considerate in their comments.
Because of the limited numbers we can take in our program which ensure only three pupils per class and a maximum number of classes limited to two we are able to keep our Chloramines (this is what causes the chlorine smell and sore eyes) very low hence reducing the potential for sore eyes from chemicals. We cannot however reduce our water temperature to 24-26 Celsius (Olympic racing temperature) because your child would not be comfortable in that water temperature at all, in fact they would not want to get into the pool and we would all have a battle getting and keeping your child to and at swimming lessons.
So the next time your child may complain about sore eyes after a lesson please keep in mind the difference be the effect of warm water and the effect of chemicals.