No Elmo as far as I know on the Sesame Street show has no brother but he does have a mother and father which was seen in his Potty Time video.
Grover also as far as I know has no brother or sister on the show although I do remember seeing Groves father one time but it's been awhile.
Elmo and Grover are just puppets so in reality they don't have any relations but they can on the show.
Still Elmo and Grover and all of those characters are awesome and even as an adult I love them and I think of them as real even though they are just fabric and foam.
They are some great puppeteers that control those puppets.