I'm not sure specifically who Ty is without more context from the fanfic, but he's clearly someone who has a connection with Amy and is willing to take care of her when she's sick.
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.
Another possibility is that she's been under a lot of stress lately. There could be a lot of things going wrong at the same time on the ranch, like financial problems, problems with the animals, and then getting sick on top of all that is just too much for her to handle, so she freaks out.
In this fanfiction scenario, Ty and Amy would be in a tough situation. They'd likely rely on their instincts as parents. They might have a stock of basic medical supplies at home. Ty, with his practical skills, could try to make the baby as comfortable as possible. Amy, on the other hand, would be more focused on the emotional aspect, soothing the baby with gentle touches and soft words. They'd also be thinking about whether they need to take the baby to the doctor. If the symptoms persist or get worse, they would surely rush to the nearest hospital or clinic, all the while praying that their little one gets better soon.
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 this fanfic, it might be that Amy Fleming yells for Ty out of anger. Maybe Ty did something that she didn't like, like making a decision about a horse without consulting her. Her yelling could then lead to a big argument between them that eventually resolves into a deeper understanding of each other.
Another possibility is that she got into an altercation with someone. Perhaps there was a conflict with another character, and things got physical, resulting in her getting hurt. However, without more context from the fanfic, it's hard to be certain.
One possible story could be that Amy Fleming uses her skills and knowledge (assuming she has some relevant skills in the original context) to take care of the sick little kid. She might bring the kid some warm soup, read stories to comfort the child, and call a doctor if needed.