Hi KB
Sorry your first post has to be because of something bad
Firstly, can I ask what the catfish is. It covers a number of types of fish including corydoras and plecs. Knowing which you have will help.
KH next; despite what the strip instructions may say, there is not good or bad level of KH or GH unlike ammonia and nitrite. It depends on what the water is like coming out of your tap. GH is general hardness, and is a measure of the amount of calcium and magnesium in the water. This is what we are talking about when we say 'the kettle is always furring up because the water is so hard'. This is only 'bad' if you are trying to keep soft water fish (eg most tetras, south American cichlids) in hard water or hard water fish (livebearers, Rift Lake cichlids) in soft water.
KH is linked to hardness, and is a measure of the amount of carbonate in the water. This is what is called a buffer, that is it stops the pH of the water changing. If there low KH it can get used up and the pH drops. If the KH is high, the pH will be very stable and almost impossible to alter. The only not-good KH is one that is so low it is below 3 German degrees because of the possible impact on pH. So ignore what the strips say about 10 being 'slightly high'. It just means your pH won't crash. (Mine is 3 and I have had a pH crash!)
Now to the neons.
How long have you had them, and have you got any new fish in the last month?
Are they showing any other symptoms besides the finrot and the lump on one of them, eg bleached looking red area, blue stripe looking yellowish?
The best thing initially until we have a diagnosis is more water changes than usual, say 30% every other day for a couple of weeks. This will dilute any ammonia or nitrite that might be there despite the strip readings.
I use API liquid testers, you can buy them as a master set with ammonia, nitrite, nitrate and both pH and high range pH (though you only need one of them depending on the value of your pH). On-line is cheaper than a real shop but slower getting hold of it. There are other makes as well, maybe go shopping and see what you can find. Whichever make you buy, one of the bottles of nitrate tester will need to be shaken very well, the instructions will say which one. Failing to shake it till your arm falls off is the most common cause of inaccurate nitrate results
So in summary -
Ignore what the strips say about your KH
Have a close look at your neons for anything else wrong
Do more water changes, and if you need to dose med do it afterwards. Otherwise add enough med to treat the volume of new water.
Tell us what the catfish is, please.