Is the pool and indoor pool? I have issues if I spend too much time in chlorine and if it's an indoor heated pool, the sauna of chlorine makes me sick every time. We now use an outdoor pool.
If you've ruled out contaminated tanks, bad gas, and all else, this may be the problem. I sure was for me. I went home feeling thick and headachy and the next day I was nauseous and flu-ey feeling. Every time. Once I stopped using that pool, I was fine. It may not be it for you, so please see a real doctor who counts.