If you are getting tiger barbs from the same shop, and they keep dying within a few days of going into your tank, there could be a major difference in water chemistry between the shop and your tank.
eg: the shop might have the fish in soft acid water and your tank could have hard alkaline water, or something along those lines.
It's also highly probable that there was some ammonia in the water, possibly from the new fish being introduced, or the filters not having finished cycling. And in alkaline water (your tank water has a pH of 7.6), any ammonia would be very toxic.
It is possibly a combination of these factors, and even more. Byron mentioned stress from being caught and bagged up at the shop. I have had fish die in the bag on the way home, simply because the shop employee that caught the fish, chased them around for a few minutes before catching them. Even if being chased doesn't kill them directly, the fish become stressed and if they go into a tank with different water chemistry (pH, GH, etc), or into a tank with ammonia, the combined stress kills them.
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Tiger barbs don't naturally fight to kill each other. They are an active schooling fish that naturally occur in groups of hundreds to thousands and they need companions to feel safe and secure. If they are in small groups (less than 10), they can stress out and there can be dominance issues with the biggest male bullying smaller males. But they don't normally try to kill each other.
They will also chase each other around a tank and as mentioned by Byron, that is not a problem when they are in big groups because any aggression is spread out over all the barbs in the group. But if you only have a couple of barbs, it can appear as tho one is attacking the other/s.
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Tiger barbs can be sensitive to chemicals in the water. If you have concerns you can add Activated carbon to the filter and that will absorb chemicals from the aquarium water. It will also absorb plant fertilisers and fish medications, so should not be used if fertilising plants or treating fish with chemicals.
An option is to have a container of tap water and dechlorinate it, then add a small filter with carbon to the container. Leave the carbon filter on the container of water for 24-48 hours and then use that water to do water changes on the tank. Any chemicals in the tap water will be removed by the carbon and it should minimise or prevent the chance of the fish dying from certain chemicals in the tank. You will also be able to fertilise plants and or use medications if you need to.
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re: the bloated discoloured dwarf gourami.
Dwarf Gouramis (Trichogaster lalius) have 2 main issues. The Iriodvirus and Tuberculosis (TB). All gouramis and Bettas can have one or both of these diseases, and the diseases can be spread to any fish that is exposed to the disease organisms.
The Iridoviruvs is a stress virus that damages internal organs and causes sores on the body that develop into major infections and kills the fish. Keeping the fish in optimum health and in ideal water conditions helps reduce the chance of this disease occurring, but when the fish get old or stressed, the virus can flare up and kill the fish.
Tuberculosis is a bacterial infection that slowly grows in or on the fish's internal organs. After a period of time, (6-12 months, sometimes longer), the bacteria cause an organ to rupture or fail and the fish dies from internal organ failure. The most common signs of TB include: fish suddenly bloat up, stop eating, breath heavily at the surface or near a filter outlet, do stringy white poop, and die within 24-48 hours of showing these symptoms.
There is no cure for TB in fish.
Any fish can carry TB or the Iridovirus for months and there is no way of telling if they have the disease until it affects them. And because there is no cure for them, the best thing to do is avoid keeping fishes that are known to carry these diseases. As mentioned by Byron, if you can find someone locally who is breeding dwarf gouramis, then their fish should be free of the disease. But any dwarf gourami from Asia could carry one or both of these diseases. This is because a lot of the breeders in Asia have these diseases in their ponds, and their fish are infected. And a lot of the exporters in Asia have the diseases in their holding facilities, so even if the fish were clean at the breeders, they can become infected at the exporters.
If you want small gouramis there are plenty of different types to choose from, just avoid the common dwarf gourami (Trichogaster lalius) or any of its colour forms, and you should be fine. If you really want to keep this species, then keep them in a species only tank so the only fish in their tank are the dwarf gouramis.
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On a side note, the Iridovirus does not affect people. However, TB can infect people if they have cuts or sores on their skin and they get contaminated water on them. Your fish might not have either of these diseases but you should err on the side of caution and wash your hands and arms with warm soapy water after working in the tank. And if you have any cuts or scratches on your skin, do not get tank water on them, and wear a pr of rubber gloves to prevent aquarium water getting on your skin.
If you get any sores on your hands or arms that don't heal within a couple of weeks, talk to your doctor and tell them you keep fish and have concerns about TB because one of your fish might have died from that. The doctor should take a swap of the sore and send it off to be cultured. Wait for the results before taking any medication because if it is a TB infection, only certain anti-biotics will treat it, and you need to know exactly what strain of TB it is.
While you wait for the results from the swab, you can apply raw honey directly to the sores and put a Band-Aid on it. Rinse the area twice daily and reapply the honey and Band-Aid and see if that helps. Honey can heal a lot of minor infections and whilst it might not help with TB, it can help with some other infections.
Having said all this, most healthy people never develop TB infections from working in their home aquariums. I had TB in my tanks for years and never had an issue. People that are most at risk of developing localised fish TB infections in their skin, are people with immune deficiency disorders, HIV, Hepatitis, Diabetes, Heart Disease, etc.
Just wash your hands and arms with warm soapy water after working in the tank and avoid getting aquarium water on damaged skin, and you should be fine
