I have asthma and I absolutely cannot handle chlorine, even chlorinated tap water or laundry bleach. We have a well so no chlorine. Maybe you can find a pool that doesn’t use it, some use silver things, I swam in one once. Totally nice fresh water.
I’ve thought about switching our pool over to salt water. I need to look into it. Another option is baquicil. A guy at a former job used it and it sucked. He hated it.
If you have allergy induced asthma get the damn shots. I got them one in each arm for 7 years, age 5 to 12 courtesy of the Air Force. If I merely touched any animal I’d be in the hospital for a week with IVs in each arm. Fun stuff. Now I have a cat and a Great Pyrenees.
-SB