If your kit can't test CYA, ask a reputable pool store to test it and report it here. Just don't buy everything they are going to try and sell you. Bleach doesn't add CYA but something that might have been used last year might have. So get it checked. We really can't advise you very well how high to take the chlorine without knowing that level.

Test kit literature is wrong. Chlorine levels needed to sanitize a pool are dependent on the CYA level. Take a look at the Best Guess Table in my signature below. (It is not a guess, it is factual.) Take your chlorine up to 4 is not adequate when you are trying to clear a pool. For now, take it on up to 12ppm and try and hold it there without letting it yo-yo up and down. Test as many times per day as you can (minimum of twice, more is better) and each time, add enough bleach to get the cl back up to 12. If you tell us the volume, we can help with amounts of bleach to add. As a reference, each quart of 6% bleach will add 6ppm to a 10K pool. Until we know your volume, you can use that to help you determine how much bleach to add to get back up to 12ppm.

I still suspect that your DE filter may be the problem because DE should not cause a pool to become cloudy. When added to the skimmer, the DE should stay in the filter. If the filter is in disrepair and it causes the DE to shoot into the pool, that would cloud a pool. That is why I suspect the filter may be the problem, but I am not the DE filter expert around here. Hopefully someone else will chime in on this thread about that issue.

Repost with CYA level when you get it tested, and with volume.