I heard that listerine baths help with skin fungus. Is it true?

No. I have not heard of this and sounds dangerous to use a product inconsistent with its intended purpose. Please see your md and/or dermatologist for a proper diagnosis and treatment.
Maybe. There are effective antifungal creams available containing terbinifine, Miconazole and undecalynic acid. The problem is that fungus can recur. The use of listerine is unproven. If the otc do not work there are prescription oral and topical agents for fungus.