No, she doesn't have a brother in the finished movie.
However, according to some behind-the-scenes info, she was originally going to have a brother named Mheetu. However, he was scrapped pretty early on in production (I think this was before the film was even called "The Lion King" - this was back when it was still "King of the Jungle")!
I think there are a few bits of rough concept art and character designs floating around of Mheetu. As he was discarded at an early stage during preproduction, nothing is very detailed and I'm not sure how much of a personality he had. He was actually one of many characters that didn't make it to the production of the film.
It's pretty normal for this sort of thing to happen in animated movies. Things can change pretty rapidly in preproduction quite a lot and there are often characters that never end up being used.
It is interesting to think about, though! Makes あなた wonder what kind of an impact his role would have had in the story, and of course amongst fans.