I'm not going to address the chlorine issue, others have already started you on the track to fixing that part.
I do suggest that you get a proper test kit however, it is essential.
this is why sand filters are the way to go...........
I have been battling cloudy water after swimming all season. I know my water chemistry is good, and the cloudiness is the result of swimmers stirring up fines that my filters couldn't catch because I too find the water is clear the next day after everything settles to the bottom.
Two nights ago a member here asked me what my filters were made out of and told me about walmart's Intex type filters (two pack). I just happened to have a pack of those in the garage. The filters I was using were Intex brand, and looked like dryer sheets (spun fiber). The walmart filters have tiny dots all over them (like a miniscule version of a solar cover).
I changed out the filters w/the walmart ones and brushed the pool debris up real good. 3 hours later I could not see any fines on the floor. Water very clear. I cleaned both filters yesterday, replaced them and vacuumed the large stuff. Today, the floor is completely free of fines. WOW!
If you're seeing cloudy after swimming and you have filters that look like dryer sheets... try changing to the walmart brand. I honestly can't believe the difference.
Hope this helps.