Yes, the medication (Erythromycin) that you used is an anti-biotic and killed all the bacteria in the tank and in the filter.
The filter will take about 1 month to rebuild the beneficial bacteria you need to keep the water clean. It could take longer tho.
The only way to see if the filter has established is to test the water (or have a petshop test it) for ammonia, nitrite and nitrate.
When fish food and waste break down in the water they produce ammonia. After a couple of weeks some good bacteria will have developed in the filter and they eat the ammonia and convert it into nitrite. A couple of weeks later you get more bacteria that grow in the filter and they eat the nitrite and convert it into nitrate. When all these bacteria are living and working in the filter there will be no ammonia or nitrite in the water and the filter has established or cycled.
Until the filters have establishes, you should only feed the fish once every second day, and only give him as much food as he can eat in 2 minutes. Then remove any uneaten food from the tank. And you have to do the 75% water change 3-4 hours (or within 8 hours) after feeding him until the filters have established. The water changes must be done even if he eats all the food.
Anything that breaks down in the water will produce ammonia. This includes fish food, fish poop, rotting plants, anything. The water changes will keep the ammonia levels low while the filters grow the bacteria they need to keep the water clean.
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You can use the same brand of cartridge for the filter if you like but it is not a very good filter media. However, if that is all you can get then use it. If you can get some sponges then they will last longer and won't need to be replaced until they fall apart in the future. Whereas the cartridge has carbon in that needs to be replaced. And each time you replace the cartridge, you lose a lot of the good filter bacteria.
Different filter cartridges will not make any difference to how long the filter takes to establish.