White water mold is possible to get in a chlorine sanitized swimming pool, it's just rare to see. It's actually a fungus that usually starts off inside pipes and likes darker/shady areas of the pool (like mustard algae). It can form films like bacterial biofilms that are hard for chlorine to penetrate.
To the OP - it sounds like your pool has not been properly chlorinated and that, whatever testing and chemicals you are doing is inadequate. White mold is a symptom of pool water that is not properly sanitized. Suffice it to say that no one should be swimming in the pool until the problem is fixed.
If you read through our site, you will see that we are a DIY forum when it comes to water testing and chemistry. We do not rely on pool stores as their testing is often wrong. We also do not use high priced pool store chemicals which are often just highly marked-up versions of stuff you can find in Walmart and grocery stores. If you want our help then you will need to ditch the pool store and BioGuard chemicals and commit to the TFPC Method of pool care. That starts with owning your own test kit (we recommend you get one of the two we list in Pool School) and testing your water yourself.
If you post test results from one of those kits, then we can help you easily solve your water problems.
Good luck,
Matt