paragraph 3:

did some ultrasonic inspection to her leg --> did an ultrasound scan of her leg

the nurse administered--> a nurse administered

Before their taxi arrived home, I had already returned home after giving classes to my student at the university. As soon as they (my wife, my mother and my child’s aunt) brought my child into the door of my home, I found my child breathing desperately, trembling/jerking with dry lips. We immediately brought the child back to the hospital to the emergency room, but it took the taxi for about half an hour to arrive at the hospital -->

Before they got home, I had already come home from class. As soon as they (my wife, my mother and my child’s aunt) brought my child home, I found my daughter breathing desperately, trembling/jerking with dry lips. We immediately took her back to the emergency room of the health center, and this whole period of time was about half an hour.