The problem with diagnosing problems in fish is we have almost no tools. This is a perfect example of how difficult things can be as I will list several reasons why your fish looks as it does. But first I need to comment on your information.
Using only distilled or reverse osmosis water in a tank will harm and eventually kill fish and plants. Therefore I have to assume you have omitted details on how you remineralize the water. You also mention nothing about adding ferts for the plants. Also, your water change routine is not sufficient, more water needs to be changed more often. All my tanks get a 50% water change weekly. You need not vacuum the whole tanks every week but you should change water every week. You can vacuum a part of the tenk every week however and over a few weeks you will cover the entire substrate this way. The more live plants one has in the substrate, the less often one needs to vacuum
1. Constipation: If the fish is blocked, it will swell. It will also not be pooping and will stop eating. Usually you notice it will take in a some food but then spit it out. Some believe Epsom will act as a laxative, other do not. What is certain is adding it will raise the hardness of the water, That is not usually a good idea so it is best done in a hospital tank with only the affected fish, The epsom needs to be added over a little time to avoid a rapid large change in GH. Here are a few other relevant thoughts on this
Some fish are more susceptible to constipation than others. Usually fish with more compressed bodies like angelfish and silver dollars. Symptoms are loss of appetite and swelling of the body. The cause is almost always diet.
Usually, with a change of diet, the condition rights itself. But in stubborn cases try dried food that has been soaked in medicinal paraffin oil. Glycerol or castor oil may also be used. If the diet is changed on a regular basis and live foods offered occasionally this condition may never occur.*
2. Internal parasites or worms can cause the same thing. Often these are only associated with wasting, but they can also cause blockages in the fish, These would require medications to fix. Knowing exactly which one might work would depend on knowing what needs to be killed and that takes tools most of us lack. So one must go with the best guess. If this is the problem my bet would be the problem may have come in with with the twig cats or perhaps plants recently added.
3. Internal infections can also cause swelling. However, the swelling is a symptom and knowing what the infrction is and where can be difficult. Internal swelling can cause blockages. One needs to treat the infection with antibiotics. Here are two examples:
Symptoms: Bloating of the body, protruding scales.
Dropsy is caused from a bacterial infection of the kidneys, causing fluid accumulation or renal failure. The fluids in the body build up and cause the fish to bloat up and the scales to protrude. It appears to only cause trouble in weakened fish and possibly from unkempt aquarium conditions.
An effective treatment is to add an antibiotic to the food. With flake food, use about 1% of antibiotic and carefully mix it in. If you keep the fish hungry they should eagerly eat the mixture before the antibiotic dissipates. Antibiotics usually come in 250 mg capsules. If added to 25 grams of flake food, one capsule should be enough to treat dozens of fish. A good antibiotic is chloromycetin (chloramphenicol). Or use tetracycline. If you feed your fish frozen foods or chopped foods, try to use the same ratio with mixing. As a last resort add at most 10 mg per liter of water. Also, if unkempt conditions are the suspected cause, correct it.*
4. Egg bound if the fish is a female. Here the fish makes eggs and is unable to expel them. The result is the fish swells. Some folks may try and give a fish a "squeeze" to try and force them out, I am not a fan of this as it may cause more harm than good. Often the fish will gradually reabsorb the eggs and correct the issues naturally.
My best guess here is the problem is likely constipation brought on by diet. You did not mention what or how often you feed your fish. I know some of yours need veggies or algae and other are more omnivorous and need meaty foods. This sort of problem would have shown up sooner had the cardinals brought the problem in when you got them. If the issues is something contagious, then other fish would likely be showing a problem as well. This like parasites or worms usually spread as will many infectious diseases.
All of the above should be taken with a grain of salt. Remotely diagnosing fish without a ton of information is difficult. As I see it there are two basic problems you need to consider. Despite a desire to save/cure the fish, failing to do so is not a great financial loss. If the fish has something that will spread is the greatest danger. One sick fish is sad, a whole tank of them is a tragedy. You may want to treat this fish in an H tank rather than risk exposing the other fish any longer than they may have been. The other alternative is less pleasing and that would be to euthanize the sick one to curtail the potential to spread certain things to the other inhabitants.
I am not sure I have helped you beyond showing how these things are often not so simple to figure out. This is especially true when trying to do it remotely. Often as fish keepers we are faced with problems we cannot determine how to fix. All we can do is or best guess. protecting the other fish may be more important than being able to cure the sick one. these decisions are never easy. At least when it is something like Ich or worms hanging out of the fish's anus we can see, accurately diagnose and treat with success. other times we are simply lost and the best option is to protect the rest of the tank.
Finally, I would ask if you have perused the section on the site here on diseases? You can find it here http://badmanstropicalfish.com/fish_palace/tropicalfish_disease_identification.html
* all quotes from http://animal-world.com/encyclo/fresh/information/Diseases.htm