. . . membership updated.

New filter cartridges will help, but a bigger pump by itself will not. If you want to improve filtration, but a pump + filter like this:
Intex Sand Filter Pump 2900 Gallons (GPH)
But, for $47, I'd absolutely start over . . . even if you get the new pump. It's hard to clean up algae, and harder to clean up chemical hobo soup, which it sounds like you have.

Good luck!