Diagnosing diseases is one of the more difficult things in this hobby. Commercial operations will dissect an ailing fish out of the group, stain slides, use a microscope, and by doing this come up with a better idea of what the issue is. This is more likely to point towards the proper medication. Obviously doing this with a single pet fish is not an option.
The best approach in a situation such as has occurred here is an educated guess, and treat with a broad range medication to treat what is the most probable issue. Osmotic pressure is much easier to understand than the identification of bacteria with a microscope, and is obviously less invasive. In any case involving bloat you can use this to your advantage; thus the addition of epsom salt to the tank water, or as a dip. Distilled or RO water accomplishes the opposite of this, and is not something I would ever suggest for a freshwater fish with any sort of swelling.
If you suspect there are bacteria in your tap water that may affect fish, which I have never heard of but may be possible, I would give the replacement water a quick boil, let it cool and aerate it before the water change. Personally if I suspected bacteria such as that in my tap water I would be hesitant to consider it potable water.
One of the biggest problems with antibiotics and fish is resistant strains of bacteria. All antibiotics are poisonous to something, in a best case scenario we pick the drug and dosage that will effectively eliminate the bacteria with little or no harm to the fish. The more potent the drug the bigger the risk to the fish in most cases. In any field of medicine the least invasive and damaging course of treatment is chosen first. In this case it would be the epsom salt, followed by antibiotics such as Maracyn and Maracyn II. There are more effective antibiotics out there, if you have the proper disease identification, and usually at a higher cost. Maracyn is one of the most easily obtainable medications in the US, and is usually the most logical starting point with a disease that does not have a positive bacteria definition.
The biggest problem with Maracyn comes with the box; the instructions. With all other living things, humans, other mammals such as dogs and cats, antibiotics are given daily for 10-14 days. Five days will not cut it for antibiotics, and this in itself can, and is the probable cause of drug resistant bacteria strains. Most bacteria that cause disease are water borne, there are no water change instructions with any of the Maracyn antibiotics.
The solution? Large daily water changes, 50% or more, and a redose, every day for 10-14 days. If Mardel put these instructions on their medication they would not sell much; everyone is looking for a quick fix. Unfortunately bacteria don't understand a quick fix, can be quite resilient, and after the short dosage period reappear, often in a form that is resistant to the drug that was used.