Leena,
Your pool is about the same size as mine and your sand filter is 24" or 30" diameter? about the same as mine but your pump is way too big. For excellent filtration you want a slower flow not a fast one. There is no such thing as a high rate sand filter! I don't care what marketing department plaster over the advert there isn't they become high rate strainers and as you have described the debris, skin, insects etc get such a rough ride they break up and return to the pool. All you are doing is paying for a lot of electricity to achieve very little. Bigger pump = worse water. Commercial pools don't try and filter at the speeds domestics do. it's another of the pool industries wrongs.

Take a look at my signature, I run a similar sized pool on a tiny pump. Actually pumping is less than 0.1 hp, around the amount of a lightbulb in electricity per hour. You are using around 30 times more to achieve the same but your water quality relies on skimmer socks. Although I run my pump 24/7 as the electricity bill is so low I can afford to and that means there are no overnight leaves, dirt etc going to the bottom of the pool. The only downside is you have to empty the skimmer more often because they are actually doing what you want them to do, collect surface debris.

I sold my pool cleaning robot, didn't need it anymore and people are familiar with that little dust cloud in front of a manual cleaning head? The one where the water starts off clear but by the time you have finished cleaning there is a slight haziness to the water? That doesn't exist any more, there is no dirt to cause it.

Go tiny on your pump, if you have water features you may need more but if like me you just filter, go tiny.