The first thing you need to do is to get a much larger tank. Like we already said, 20~30 gallon minimal.
Then get a filter. Aquarium filter and home drinking water filter are completely different and they do different things. They are no substitute of each other.
Your drinking water filter only has activated carbon in there and it has no filter media like an aquarium filter for nitrogen cycle to take place.
So get yourself a real aquarium filter.
Which water conditioner are you using? It should have the name on the bottle.
Tap water is perfectly fine if you use aquarium water conditioner.
Aquarium filter is used for nitrogen cycle. If you read the article - fishless cycle, which we had posted link above, you should know it is no substitute for water change. Water change is used to remove the final produce of the nitrogen cycle - nitrate. We typically do 30~50% partial water change once a week in a well established tank just to remove nitrate, restore water buffer, etc.
Your current situation is you have a tiny fish bowl that is unsuitable for the fish, and you have no filter to speak of, nor the tank is cycled. You must quickly fix the first two, then hopeful the best that the fish can survive through nitrogen cycle. So you need to do water change every day as we suggested. By using Prime as water conditioner, it helps the fish to survive better, although nothing can guarantee your fish will 100% survive.
Good luck! 
| 
