Tea Tree Oil is the ingredient that seems to cause the problem in the Melafix and Bettafix. The Pimafix contains Clove Oil which is an anesthetic to fish and also is use to put
euthanize them. If used over a period of time it can make the fish dopey and overmedicated and lethargic and since it does not evaporate can cause death the same as if you were wanting to put your fish to sleep due to a horrible illness. Any herbal medications which contain an oil would actually be questionable for fish with Labyrinth organs as they need the surface of the water to be clean, and that means oils or other substances that would coat the surface of the water would keep them from being able to use that organ to breathe air which can cause the fish to drown or at the very least to cause the Labyrinth organ to fail. These meds just do not work for any of the fish that are included in the family of fish that the bettas belong to as well as the Pencil fish who is technically not in the family but still for some reason has the same reaction to these meds.
We have had bettas on this forum die from use of these meds and unfortunately one of my favorites was one of them. Natalie also lost a very lovely boy from the use of Melafix. We were unaware of the information about these drugs until our fish were already being treated with Melafix. The Pimafix was added to the list when we became aware of the build up potential for the Clove Oil.
You are fortunate to find Triple Sulfa and Tetracycline. They will treat most things and the Triple Sulfa is my med of choice for finrot and a few other nasty little diseases as it generally makes quick work of them. The bad part of this is it is limited on how many times it will work on one fish so if the little one is particularly unhealthy you are going to need at least two antibiotics as you cannot keep using the Sulfa over and over for different problems. It will stop working.
A lot of things will be treatable with Clean Water and warmth. Ich responds best without meds, just raising the temperature. If you catch finrot or some of the skin disorders as long as they do not involve a fungal infection, clean water and conditions (cleaner than usual and more frequent cleanings) and a slight raise in temperature can and does sometimes do wonders. Tears in fins are done the same way after you find out what they tore the fin on or what did the damage. Some of the parasites will leave the body of the fish just by raising the temperature of the water and stay off with the temperature over a certain level (usually 82 to 84 F or 28 to 30 C) and then you just need to keep it at that level long enough for the lifecycle of the parasite to complete and to make sure no new hatchlings of the parasites are still around to settle back on the fish when the temperature is decreased.
I am making a book here and all you asked about was the ingredients. So sorry. I hope this answered your questions.
Rose