Amy Fleming and Ty are likely characters from a particular series or fandom. They could be characters who have a relationship, perhaps friends or more than friends. Without more context, it's hard to say exactly who they are in the grand scheme of things, but they must be important to the story if Amy is yelling for Ty.
Definitely Ty Borden. He and Amy have a special relationship, so he would be deeply concerned about her illness. He could be the one running errands, getting medicine and making sure she has everything she needs. Georgie could also be a main character. She could be helping Lou with the ranch work and also spending time with Amy, telling her stories to keep her spirits up. And then there's Spartan, Amy's horse. Spartan could be acting strangely because he senses something is wrong with Amy, and his behavior could be a part of the story as well.
In the fanfic, her character could be shown in a more introspective light. Since she's confined to her bed with the flu, she has time to think about her life, her relationships, and her future. She might have flashbacks to important moments in her past and realize things about herself that she hadn't before. This could lead to some character growth once she recovers from the flu.
Sarah was significant as she was Abraham's wife. She was part of God's plan to create a great nation. Even though she was barren for a long time, her eventual pregnancy and the birth of Isaac were important steps in fulfilling God's covenant with Abraham.
I'm not sure exactly who Sarah is without more information from the story. But she is likely a person who has a weight problem and is the focus of the '600 pound life' story.
There might be a mysterious stranger. This person could be passing by when they hear Amy Fleming's screams for help. They could have some special skills or knowledge that can assist her in whatever situation she's in. Another possible character could be an authority figure like a sheriff or a teacher, depending on the setting of the fanfic, who has the power to protect her.