Quickly:

1. Using the hot tub as a test bed is a good idea, up to a point.

2. That point has to do with UV. There is a LOT of evidence that chlorine + UV (sunlight) breaks down problem causing chlorinated goo, that will REMAIN in the pool with chlorine alone. Ozone breaks down some of these . . . maybe, the evidence I've seen is ambiguous . . . but apparently not to the degree that chlorine + UV does. SO, a COVERED hot tub is not the best test.

3. Get the K2006. We're going to need it, to track down the problem.

4. Softeners replace other metal ions with sodium ions. This does not reduce TDS. I'm not sure about carbon.

5. We're going to need your water company's test results. These should be online at your water company's website.

6. Baquacil is problematic. But UNLIKE Nature2 or ozone, it IS a sanitizing system. In Florida, you need to drain your pool annually AND replace your filter media (sand, cartridge, DE) annually. If you do this Baquacil will work OK in pools that are not heavily loaded. But, you can NOT use it wth ozone, Nature2 (copper) or chlorine.

7. Carbon strips free chlorine. But, it does NOT strip monochloramine so well, and MC tends to be substantially more irritating than chlorine. Get the K2006, so we can see what's going on.

8. I've said enough now, so this won't surprise you: several of us have looked EXTENSIVELY. There is ZERO credible evidence that anyone is allergic to, or experiences respiratory effects from free chlorine in pool water. The absence of evidence is not proof. But it's more than enough reason to focus on other chemicals, including chlorinated by-products.