my suggestions:

paragraph 1:
preventive medicine for animals --> preventive Veterinary Medicine from Huazhong Agriculture University

paragraph 2
My child, Liu QianQian (刘谦谦), was two years and 5 months old, born in the U.S.A. She had a fever and running nose at night on 4/20/2009 -->
My daughter (or son depending on gender), Liu QianQian (刘谦谦), born in the U.S.A., was two years and 5 months old. She had a running nose and a fever in the night of April 20, 2009.

My wife, my mother and I brought my child, by taxi, to the emergency care of Women and Children’s Health Hospital of HuBei Province. -->
My wife, my mother and I took my daughter, by taxi, to the emergency room of Hubei Women and Children's Hospital (or Hubei women and children's health center).