Please do what OFL says, don't remove him or do more then a 50% water change. BUT make sure the water change is using dechlorinated water. That's so important.
I added in how to acclimate your fish to new water and linked some articles. When adding in the new dechlorinated water, you can use the same idea below, add it in slowly. cant stress how important it is to dechlorinate the water though when using tap water.
Do you have a tap water dechlorinator yet missmayr? (what brand?)
If you don't have one that is why he gets sick right after a water change in tap water. Another reason is the temperature could be very different. Another is if you are using bottled water and try to change him to tap suddenly he can go into shock from the sudden difference in PH.
Also yes he may be so skinny because he needs more food, or yes there could be another problem. Did you notice what his poop looks like? Is it stringy and light colored/white, or are they round brown ball type shapes?
Don't remove your fish to a different container in your personal case as advised.
One way to do a water change over: (acclimating him to different water.)
1) cup your fish gently into a small fish safe container in the water he is currently in. Leave some room in the top of the container so you can add in water, but leave enough room for your fish to be comfortable in during this process.
2) change water in his home tank completely, refilling it with water the same temperature or as close to the same temperature as you can get from the tap. Add drops of tap water dechlorinator as manufacturer directs on bottle per gallons of water. to the new tank water. (most dechlorinator usually uses 2-3 drops per gallon or something close to that.)
3) Float the container in his tank and wait until the water in both containers is the same temperature.
4) take small amounts of his new dechlorinated
tank water that is fresh, and add small amounts of it to his old water, every half hour to an hour making sure you don't get any of the old water in his new. If the cup gets too full remove some of the water and keep doing this slowly. If your fish shows any distress after adding the new water stop adding it, and wait until he recovers. Adjust the amount of water you are switching him to so he doesn't act stressed when you are adding the new water. Maybe start with a tablespoon of water to the old and wait. If things are ok next half hour to an hour, you can do another tablespoon or maybe 2 tablespoons if he is still acting ok. (The amount of water would kind of depend on the size container. I think it's something like 10%) making sure the water is dechlorinated is important before adding any to anything the fish may come in contact with!
5) If the container gets too full gently dump some of the water out (this can be dangerous if he jumps!!) or remove it with your fish turkey baster tool, or scoop some out with a plastic/ foam cup.
6) Keep doing this until your fish is in 100% of the new water and his old is entirely diluted or changed out. How long this takes really depends on how stressed your fish acts to the new additions of water. With him being so miserable I would go really slow. (That is only my opinion though)
It's called acclimating your fish. I will try to link some good posts about how to do this with better directions for you. The slower it is done the safer it usually is because they are less likely to go into shock from big differences in the water. This really only needs to be done once to help your fish adjust to the water he will be spending his life in.
Future water changes can be done simply by letting the water come to temperature in both containers and when it's the same, just adding your fish to the new water.
((Tip: If you have any gallon jugs from the grocery store that drinking water comes in you can use those to keep a supply of aged and dechlorinated water near your fish. Drink the water that comes in the jugs from the store. Then just re-use the jugs from then on for your fish-only water.))
Good articles on acclimating:
There are some threads here too on the forum on how to do this. They are not popping up in google for me atm.
If anyone knows of a better way or I am mistaken or mistyped something please correct it.
my very best wishes