Hi Teash
Well like I said it sounds like cyanobacterial algae. A slime algae that builds up due to an excess of organic load that is in the water. The build up may not be visible to your eyes but it definitely still exists. Is your filter a type that hangs on the side of the tank? If it is what is the make of it (ie Aqua Clear, Penguin/Marineland,etc...)? I need to know the type in order to direct you to the appropriate media to use inside of it, or maybe direct you to a totally new filter.
In order to kill the cyano algae you can simply use EM tablets. EM is Erithromyacin medication primamrily used to combat bacterial infections on fish, however at a light dose it kills cyano really quick as well!
If your tank contains 15 gallons you only need a tablet or two to kill the algae.
**Important Note** siphon out as much of this algae in a water change before you dose the tank with EM. If you killm all of the cyano in the tank it will release all of the contaminents it has absorbed back into your tank. That could quite possibly kill your fish and also just feed the next round of cyano algae to grow after you kill it.
Get back to me regarding the type of filter you have before you start the process. We need to address that before anything can start.
Talk to you soon!