Can a doctor mix up yeast infection with ganegrene?

No: The typical cases of yeast infection do not look anything like gangrene. Gangrene is dead flesh.

unlikely: Gangrene occurs when tissues lose their blood supply and die. "dry" gangrene is when the tissues become dry and black. "wet" gangrene is when the tissues begin to get foul-smelling and "rot". In contrast, a yeast infection is caused by yeast and the area will get red, and itchy. Interestingly, wet gangrene and yeast infection will both have an unpleasant odor but that is the only similarity.