Mold or mildew on bathroom ceiling

I have black spots all over my bathroom ceiling, I'm not sure if it's mold or mildew. We have an exhaust fan in there that quit a couple years ago and we bought a new motor for it, but I don't think it's working or helping with removing steam when we shower. Yes, it's installed correctly. We had some black spots before it quit and it just keeps getting worse. Does anyone know how to remove it from the ceiling?? I've tried clorox/water and it helped a tad.