Welcome!
You've already figured out how to post a picture, so I have high hopes for you!
Your problem isn't filtration. There was a member here a couple years back who accidentally left his filter on recirculate (bypass the filter completely) for a couple weeks. More and more crud settled on the bottom and kept reappearing even after vacuuming. He raged at the wife for letting the kids get in when they were dirty, yelled at the kids for not using the footbath, etc. etc. It was quite a comical post. Yet he never got algae, because he kept his water properly balanced. Once he found his mistake, he vacuumed it up and all was well.
If you're ready to get off the pool store merry go round, we can help. Between the articles in pool school, the forums, and your own proper test kit, you can have the cleanest sparkliest water you've ever seen and keep it that way all season at very low cost. I keep my 16,000 gallon pool open year-round and it has never turned green or cloudy, and it only costs me about a buck a day in season. Three hundred a year, plus another forty or so for test kit refills.
Assuming the water is green, your first step is to break out the credit card and go to
TFTestkits.net and order up a TF100 and get the XL option, because you'll be burning through a whole lot of the FAS-DPD test reagents while you're clearing your swamp and I'll wager large sums of money that no local pool store will carry those refills. So order them now.
Some Inspiration:
Recovering my old inspirational links Just go through and look at the pictures. You'll be impressed.
No more Pool Store Wheel of Fortune.