So you did a "fishless cycle" from October to Dec by adding ammonia to the tank daily? Remember a cycle is the forming of a nitrifying bacteria colony. That can only happen in the presence of a food source (ammonia)- a lot of people think "cycling" just means letting the water run through the filter for a while. I can understand the confusion, so I just want to make sure...
Don't change the filter media any more. Give it a good rinse in the tank water you remove at water change time then put it back. Don't use tap since tap water generally contains chlorine or chloramine, which will kill the bacteria. Replace it only when it is too junked up to clean out anymore- like once every 6 months, and never replace it all at once.
I think your problem is ammonia. I don't care how much light you put over the tank, in a properly cycled tank that is getting 3x weekly water changes there is no way you could have enough "food" available for a green water algae bloom.
In the mean time, to make it pretty, use a floculant (like accu-clear) - it will cause the algae particles to stick together so your filter sponge/floss can catch the clumps. Rinse out your media 24 hours later (again, not in tap water). The tank should be nice and sparkly clean.
