Checking the parameters will be very important. You will need to adjust the water changing schedule to an amount which will get the water to be in a safe level for the main tank.
Sometimes a fish that has been in a stressful situation and/or is also currently under stress will just not be able to recover as quickly or get better quickly.
Changing the water more often would be recommended to keep the water as perfect as possible for quicker healing.
For a tank with sick fish would probably be daily 50-100% water changes. It seems crazy, but GF eat and produce a lot of waste. Ammonia in the water and other unsafe levels of Nitrite or Nitrate are going to impair healing because the fishes body and system ability to fight off infection is lower and trying to deal with low or poor water parameters uses its resources just to survive and results in low to no progress for healing.
If the fish is kept in excellent water quality, it's system can use it's energy on the healing part instead of survival.
If you can use a plastic tote or bucket that is free from being used previously with something which could be bad for fish, just clean it out and rinse a bunch of times to make sure it has no residue and make a hospital "tank". Change the water each day. Having an extra bucket is ideal.
New (always treated) water in bucket move fish gently over.
If it is fuzzy or looks like it is getting fungal infection or red or grey or white parts increasing , not decreasing you would be better to use meds for fungus or infection.
If it is only gone but not looking fuzzy or like it is decaying then I would use a little aquarium salt maybe a 1/4 teaspoon per gallon amount and one tablespoon of Epsom salts (ES) pure no added stuff in it.
The slime coat (aquarium salt - AS) and the Epsom salt which is not actually salt but magnesium sulfate to aid in healing.
Use the AS and ES dissolved and initially add to the hospital tank gradually say 1/4 amount every 4-6 hours. After that just have that amount included in each new bucket of water daily.
When you do you water changes, make sure that the water of the hospital tank and when you change it, is never cooler than the water he is already in.
Edit: Oh meant to also say an air bubbler in the hospital tank would also be beneficial. The adjustable kind are great.