The fish is most likely gasping due to low oxygen and/or poor water quality. Also, when you changed their water did you use Dechlorinator? If not they may have been shocked by the chlorine and are stressed.
But now for an even bigger problem:
They have plenty of room! I was advised in the shop that this tank was adequate for two of them!
No. They do
not have plenty of room.
If you keep them in this tank you will kill them. The shop have lied to you. Fantails grow to about the size of a tennis ball when you keep them properly ( and at the moment you are not, no offense )
Your fish may be small now as they are only babies. But they will need room to grow into adults. In a 13 litre tank, they do not have any room at all to do that. If you keep them in there, your fish will be stunted. This means that because there is so little space, the fish release a hormone that stops their skeleton from growing. BUT, their internal organs, which are supposed to fit into a much bigger body, do not stop growing. They keep on until they are crushed into the stunted body and then they do not function properly. A very common problem in stunted fish is swimbladder disease ( where the fish cannot swim upright and rolls about upside down ) .
Do you seriously want to subject your fish to this fate? Stunted skeleton, crushed organs, drastically shortened lifespan.....
Goldfish have a lifespan of about 30 years
when kept properly .Did the shop tell you that? .
The oldest recorded goldfish lived to be about
42 years old . If you go out and buy the proper sized tank and filter ect, are you prepared to keep these fish for the next 25-30 years ?
You will need a tank of at least 40-55
gallons for those two fish. That's a tank approximately 4-5 feet long. And a decent filter. A small external cannister filter would be best for them.
You need to know this :
Goldfish are very messy. They eat a lot and crap a lot. All that eating and crapping means that a lot of
Ammonia is produced by your fish. You need the filter in your tank to be cycled. This means that the nitrogen cycle has to happen.
Ammonia,
Nitrites and
Nitrates are very bad for the health of your fish.
Ammonia and
Nitrites in particular. If you have any or high levels of them in your water, your fish will soon become ill and can develop a whole range of horrible diseases and fungal infections.
The sponges in your filter need to grow bacteria on them to
eat this
Ammonia and
convert it to
Nitrites. Then a second type of bacteria
eat the
Nitrites and
convert them to
Nitrates. You then remove the excess
Nitrates with weekly water changes.
That is basically the nitrogen cycle. But here is the thing. You are supposed to cycle the filter BEFORE you add any fish at all. If you add them to a brand new tank with an uncycled filter ( as you have done ) you are exposing the fish to the ammonia they are making. They are basically living in their own waste. Until the filter has cycled, your fish will be suffering the effects of the
Ammonia rising and falling, and the
Nitrites rising and falling.
Cycling a filter takes just over 1 month. Running a filter for 3 days with nothing in the tank and no
Ammonia to start a cycle will do absolutely nothing at all.
Go to the new to the hobby section of this website, and look at the stickied topic on fishless cycling.
If you really want to keep these fish and intend to get them a 40-55 gallon tank, then in the meantime, go out and buy a BIG clear plastic storage tub. The biggest you can get. They don't cost a lot. Put your goldfish, their current water, and the filter- basically everything into the tub and switch it all on ect. This will do fine for a temporary home while you save for, or buy a big tank. Change 25% of their water every 3-4 days.
When you get the new tank, go back and look at the fishless cycling thread, and cycle the filter using that method. It will take over a month. Then and only then can you put the fish in the tank.
If you do not have space/time/inclination to do any of this, then please re-home them or take them back to the shop.