Have you tried the methylene blue baths yet.
Shouldn't need an airstone as methylene blue puts aeration in the water.
You will just have to keep an eye on temp thats all.

What does it say on the box of tha api fungus remover.
I would see how the methylene baths go first.
How is the cory doing. is the anti finrot and fungus med still in the tank.
Bless him.
Is the fungus getting worse.
Is he laying on his side.
I would remove the finrot and fungus med from the tank with a water change and black carbon.
Then add the methylene blue to the tank.