"Bio-Bag" cartridge filter for the aquarium?

I had a 5 gallon aquarium for a month. I have about 3 too many fish that I will give a few days because I'm learning the hard way by the overhead of a tank. The problem is that the cartridge filter (with filter bag and stones carbon) was plugged and the water does not flow through it. Actually pushes water up through the cartridge compartment and tank glass on the table. I tried to clarify the original filter but that does not help at all. I bought a new box of replacement filters and filter changed everything (frame, stock market, and carbon). I am doing research and now considered not good to change the entire filter. How should I have done this in order not to disturb the bacteria or stress the fish?

The Tetra filters with Bio-Bag that I know have a foam cartridge too. This is where most of the biological filtration takes place. Is this a tank version Whisper? In all honesty, you need to get away from that 5-gallon tank to make things right with the aquarium. 10 gallons is a challenge. Things are not easy to reach about 20 gal.

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