There is actually a lot more to starting up a fish tank than most people think, but you have come to the right place for advice
. If you can't rehome the fish then you will have to do a fish-in cycle.
See your fish poop and this produces ammonia. Ammonia is highly toxic to fish, so you need bacteria that 'eat' ammonia to build up in your filter. This bacteria will then convert ammonia into nitrIte, less harmful than ammonia but still toxic to fish. Another type of bacteria will build up and this converts nitrIte into nitrAte. Nitrate is only harmful in high doses and this is why we change a good amount of the tank water every week.
Your fish are gasping because they are suffering from ammonia poisoning (which damages the gills, the equivalent of human lungs).
So here is a step-by-step guide for you.
1. Buy an API master test kit, the liquid kind. This is to test your water for said ammonia and nitrItes.
2. If you can't get the test kit immediately, keep doing large water changes every day until you do (50-90%). Make sure you temperature match and dechlorinate the water first.
3. When you get the test kit, test your water. If the levels are above zero, keep doing large water changes until it is at 0.
4. Depending on how stocked your tank is, you will need to test your water once to twice a day (or more if you are heavily overstocked).
5. Repeat steps 3 & 4 everyday until you regularly receive zero readings.
A lot of pet shops will not tell you this information as they want you to buy a tank from them, and then when the fish die all the time they want you to keep buying fish from them. It's a story that you see often on this forum unfortunately
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Can you tell us what breeds of fish you have in your tank and how many litres your tank is? This will give us an idea of how stocked your tank is.