Can a person be intolerant to swimming pools?

When I was a kid I swam a lot and would get migraines and throw up from it and adults told me it was because I was swallowing the water even though I tried not to.

I recently added swimming back into my exercise routine and to teach my kids how to swim. Every day after I take them swimming I get a terrible headache and feel generally sick and tired, sometimes a little queasy. I know I am not swallowing the water or even getting it up my nose so could it be just from absorbing the chemicals from the water? It's an indoor pool so it's not from heat or sun. I also really scrub down afterwards so it shouldn't be left over on my skin. My skin is fine actually, I don't have a rash or anything, just headaches and general crummy feeling like I'm getting sick but it's only on days I swim.

I looked online and read that chlorine allergies don't exist so wondering what others know.

Thanks!