A woman is fighting for her life after she was attacked by a family pet inside her Little Village apartment in the 2300-block of S. Whipple.The 34-year-old woman is undergoing surgery at Mt. Sinai Hospital after suffering several bite wounds. Relatives said she is in critical condition.”When I heard that the lady was screaming, she was calling, I think, the police. And then I saw another guy coming from inside screaming,” said Isabel Martinez, a neighbor.Neighbors were alerted shortly after 11 a.m. Thursday when police and paramedics were called to the apartment.”They said the lady was on the floor and she couldn’t move,” Martinez said.”I seen a lot of blood on the victim. It was pretty bad,” said Josh Nelson, a local worker.