tetras, they weren't just trying to waste your time. They don't want to be responsible for you killing your tetras. The Corys may also be bothered/hurt by heavy medication and salt.
Please continue to do as they say, remembering that your 20 gallon tank only has 14-16 gallons of actual water. It sounds like you are doing what you should do. Ick doesn't just go away over night.
It is good that you are curious about what to do. However, You and I are also probably cursed with that XY chromosome thing where we only want to "follow instructions when all else fails." ;)
In the meantime, you should already have done a partial water change; made sure the tank is running at about 80 degrees F. Don't feed them heavily. You might feed them a couple of times a day, but make sure no food is left uneaten on the tank bottom.
Treatment should continue for a week. The free swimming stage of the ick should be killed off as they emerge from the gravel. In 4-7 days they should be gone.
If you do a water change, add medication only to the new water. So add two drops for the four gallons you add. If the manufacturer suggests re-medicating in a certain number of days, do what they say. Some of those Ick medicines contain medicinal dyes. Those dyes may get absorbed some by gunk in the gravel and even by the silicone sealant on the tank joints. Or it may break down some.
I forget if you have more than one aquarium. If you do, don't move equipment back and forth. :) It is so cold outside here, I have been rinsing suspect equipment off, after I'm done with the fish, and leaving that (drained) equipment outside over night.
Food for thought. Did you introduce a recently purchased fish w/o quarantine? Did the tank get chilled recently? Either of those might explain why you had that outbreak now.
All the best!
u.s.
Christmas trivia question (not to be taken too seriously): Why do "they" think that the Magi (not really kings) were male?
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