Will levoflaxcin cure a yeast infection?

As the above
Levofloxacin is an antibiotic, what you have is a fungal infection, antibiotics cannot treat it, they will not work, the only thing they will do is make it worse.
Best thing you can do is go to the pharmacy and buy an over the counter anti fungal cream sold specifically for yeast infections, such as Canesten.

Absolutely not. Yeast is a fungus, you need anti-fungal medication. The use of antibiotics actually "cause" fungal infections due to good bacteria dying off. Also, when using an antibiotic for a bacterial infection (which you don't have) without knowing if the antibiotic will be effective, you are also contributing to the growing number of antibiotic resistant bacteria, frequently called super-bugs. Save antibiotics for confirmed bacterial infections which have been tested for sensitivity to antibiotics.

No it won't, you need an antifungal not an antibiotic.