My betta, Mica, just died of cotton wool disease.

He had only been in his new 10 gal. home for maybe a week, maybe less when this happened. I noticed the fuzzy back one day, the whole back and underside was coated the next day, the third day I was able to get out and buy meds and treated the water but he died during the night. Poor thing! My question is.... what do I do about the tank? Is it safe to put another betta in it? Do I have to do a complete water change or maybe just 50%? Should I keep treating the tank with Jungle's Fungus Eliminator and Aquarium salt? I don't know what to do and I would appreciate any advice you can give me. I have Mica's brother still in a large vase, just waiting his chance to get in the 10 gal.
Thanks for your help.