I wouldnt QT in a container, he needs the right ammount of water and filtration to get better, which you cant provide in a container.
what size is your tank and how many fish are in there?
if you dont have the test kits, you can just assume that the water is fine, even though you are doing all these water changes the water could still be dangerous. you need to go and get the test kits.
Id, put him back in the main tank, get the test kits, keep the water perfect, if you can find a good antibacterial med use that, check if you can use salt with the med (you cant with most) if you can use salt, salt to 0.1%, thats one teaspoon per gallon of water.