I'd get rid of those plants . I recognise them they're from Wilkinsons right? . I had some and they fall apart within weeks. All the tiny fronds come off and float around they're really cack.
Real plants would look FAR better and more natural, and will help use up a bit of waste. Cabomba is a good choice and very easy to grow. You just plant the stems in the gravel and leave them alone. Roots should form and all you have to do is nip out the tops when they trail across the surface.
Moss balls are another great choice and unusual looking too. You can get them in packs of 5 small ones on Ebay. Those are possibly THE easiest plant on earth to care for. Literally just drop them in and that's it ( they do float at first but will sink after a few days ) . They stay in a ball and sit there looking good.
3-4 bunches of Cabomba and some moss balls would easily it out the tank and make it much nicer for the betta.
If your filter is not cycled ( it should be ) then this is a likely cause for your cloudy water. Bacterial bloom .