I'm not a professional, so I can't really answer about her asthma symptoms, although my daughter has asthma and it's never affected her. I can though tell you about non-chlorine pool sanitation from experience, and its not good. When we bought our pool, I decided to go the Baquacil route (they've changed the name I think, so I don't know what it's called anymore.) First off it is VERY expensive. One gallon of sanitizer can be as much as $75.00.
The first year of using it, everything was fine, except for the expense. Closed the pool for the season. Opened up the pool the next year and everything looked good. Looks can be deceiving. Added the proper treatments, took the water to have it tested and was told everything was good to go. My daughter and her friends got it and stirred it up and they said everything felt slimy. Next thing you know there was white stuff floating everywhere, looked like wet tissue paper. Nasty! Went back to the pool store and was told it was white water mold and I needed more sanitizer and some other special non-chlorine stuff to clear it up. Vey expensive stuff. Now the sanitizer runs about $75 a bottle, they said you only have to add it once a month (yeah, right), try about once a week to keep your levels up. And the other stuff I forget what it was even for, but it was about $20 a bottle a couple times a week. Not cost effective at all.
I converted my pool the next summer to chlorine and have never looked back. I won't tell anyone how to sanitize they're pool, but I personally would never recommend these products, unless you are very wealthy and have a lot of spare time to keep up with it.
Please read a few of the stories under converting your pool from Baquacil to chlorine, just to get a feel for what other people have dealt with using these products.
