Most fish health issues are caused by poor water quality and a dirty tank. Cleaning the tank, gravel and filter dilutes any gunk and nutrients (ammonia, nitrite, nitrate, etc), and it dilutes the number of disease organisms in the water. The cleaner water and fewer disease organisms gives the fish a chance to heal itself and reduces the chance of health issues affecting other fish in the tank.
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The only thing you need to have on hand is rock salt, dechlorinator and some Activated Carbon.
Salt treats minor fungal and bacterial infections, gill flukes, anchorworm, and some external protozoan infections (Costia, Chilodonella, Trichodina).
White spot and Velvet can be treated with heat (30C or 86F for 2 weeks).
Carbon can be used for a possible poisoning.
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A first aid response for fish should be to clean the tank conditions up.
1) Test the water quality.
2) Wipe the inside of the glass down with a clean fish sponge.
3) Do a big (75%) water change and gravel clean the substrate every day until you identify the problem.
4) Clean the filter.
5) Take pictures of the fish and start a thread on a forum asking for help.
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API General Cure contains Metronidazole and Praziquantel. Metronidazole is used to treat people for internal bacterial and protozoan infections. Praziquantel is used to treat tapeworm in dogs and cats.
Erythromycin is an anti-biotic that should only be used on known bacterial infections that have not responded to normal fish medications.
Improper use and mis-use of anti-biotics has caused drug resistant bacteria that kill people, animals, birds, fish and reptiles.
Nobody should have anti-biotics at their home unless they were prescribed by a doctor for a confirmed medical condition.
Anti-biotics break down quickly when exposed to heat or humidity/ moisture and need to be kept in a cool dry dark place away from children and animals.
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Melafix and Pimafix are not worth having on hand.