Based in your statement that your tank is cycling again I would assume you are not totally clear on what the cycle is. A tank is in continuous cycle. To help you understand what is going on and better prepare you to deal with this I would offer this.....
The cycle is the process that takes ammonia from the water, changes it to nitrite and then changes nitrite into nitrate. Ammonia and nitrite in small amounts are deadly to fish. Nitrate can be also if allowed to reach high levels.
Here is how the cycle works. Ammonia is created by decaying uneaten food and fish waste. If ammonia is present in the water a type of bacteria will start to grow by consuming the ammonia. The waste product of that bacteria is nitrite.
If nitrite is present another bacteria will start to grow by consuming the nitrite. The waste created by that bacteria is nitrate. You get rid of nitrate by removing a portion of water and adding new salt water with no nitrates in it.
While your tank was beginning to cycle the colonies of bacteria grew to a size that could consume the ammonia and nitrite. By adding so many fish, the quantity of ammonia and nitrite grew beyond what the bacteria could consume. That bacteria is eating as fast as it can. The only solution is to increase the amount of bacteria.
We increase the amount of bacteria (naturally) by only adding livestock slowly. Add one fish and ammonia only increases a little bit. The bacteria has a bit more food so the colony grows enough in a short period so that it can handle the little increase. After a week or too, you are back to a stable situation and can safely add another fish or two.
There does come a point where there isn't enough available surface area for more bacteria and adding more fish will cause major problems. That is why the size of the tank and the amount of live rock plays such a big role. A 10 gal tank with 10 pounds of live rock can only support a small amount of livestock. A 100 gal tank with 100 pounds of live rock can support greater amounts of livestock.
I hope that helps. As others have said, you are in a situation at the moment where you can't wait on Mother Nature. Using prime and stability would help but I think a better solution would be to rehome most of those fish. Maybe just keep 2 for now. The store may take them back and give you store credit.
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