It can be difficult to spot signs of stress in fish. Bear in mind that fish aren't 'domesticated' in the same way as a dog or cat, and many wild animals will not show any signs of stress or illness, as it can attract predators.
What stress does do is weaken the fish, including its immune system and slime coat, so that infections like fungus, fin rot and whitespot, which a healthy fish would be able to fight off, can take a hold.
One of the most vital things in fishkeeping is 'cycling'. Cycling a tank means growing a colony of good bacteria in the filter that eat the toxins from the fish's wastes. Until those bacteria grow, those toxins (ammonia and nitrite) build up in the water. In a small volume of water that can happen
very quickly, and it's why you need to be doing large water changes, making sure the new water is warmed and dechlorinated.
I'll be honest with you (please don't take it personally; like many people you've probably been given terrible 'advice' from your fish shop
); you're unlikely to be able to keep these fish alive if you don't move them. In an uncycled tank that small, the level of toxins, and the stresses on the fish, are going to be overwhelming.
If you can get them into a larger volume of water (and, like I said, even a plastic storage box will do; you can use your current heater and filter), keep the water clean with plenty of water changes and monitoring with test kits, add some live plants (to help absorb any excess ammonia while the filter cycles) you
might be able to save them. In their current tank.. well, you're almost certainly going to lose them all, I'm afraid.