K.B.
If your child is the only one that was affected then this is NOT a chemical burn from that place. A chemical burn will happen EVERY place that the chemical touched, so it would NOT be just where the trunks were but wide spread across the body or whatever part touched the water (unless washed off and treated). I use to work at a public pool and there are VERY strict rules to follow in the amount of chemicals to go into the water (and THEY HAVE TO USE them to have a public pool). At the place I worked we tested the water before we opened, we tested/checked the water around lunch time, and then again at closing time.
You can call up the facility and ask if there has been reports of chemical burns. BUT morethenlikely it is because your son did not wash off after being in the pool... which should ALWAYS be done because the chlorine or other chemicals can irritate the skin if clothes are not washed off or changed after swimming (I have seen this happen hundreds of times, all a facility can do is say/post signs wash off after leaving the pool but in the end the parents/care taker is responsible for that). You can complain to the facility BUT if they are following guidelines they are in the right and the complaint they will check to make sure and maybe the note will be written down but then dismissed.
One last thing, a TRUE chemical burn will NOT stop burning unless rinsed and treated... this is a serious injury and should see a doctor/ER immediately! I have had one (not from working at the public pool but in a theatre setting) and had to go the ER to get the burning to stop because simple washing with water did not stop it just helped ease the pain.