No. It's not appropriate. This type of topic involves very private and often embarrassing bodily functions. Writing about it in a fanfic can be seen as vulgar and disrespectful to others.
Well, this is a rather strange topic. But if we were to consider it in a non - inappropriate way, perhaps the 'desperate' part could mean she's in a situation where she's lost control due to some extreme circumstances like being trapped in a very difficult place for a long time without access to proper facilities. However, fanfics with such topics should be written with a lot of care to avoid being offensive or inappropriate.
One possible plot could be that the girl has been holding it in all day due to a busy schedule and not having a chance to use the restroom. In class, she starts to feel really desperate as the teacher is not allowing anyone to leave. Eventually, she can't hold it anymore and has an accident, which then leads to her facing embarrassment and the reactions of her classmates.
Once upon a time, there was a little girl named Lily. She was still in the stage of wearing diapers. One day, she was playing happily in the living room. All of a sudden, she made a funny face and then pooped in her diaper. Her mother smelled it right away and quickly took her to the changing table to clean her up and put on a fresh diaper.
Once upon a time, there was a little girl. She was just a baby and couldn't control her bowel movements yet. One day, while she was playing in her crib, she suddenly pooped in her diaper. Her mother smelled it and quickly came to change her diaper. The mother gently cleaned the girl and put on a fresh diaper. And the girl just giggled throughout the whole process as if she didn't know what had happened.
I'm not really sure specifically what that exact story is about as it could be a very strange or made - up scenario. It might be some sort of fictional or even a shock - value type of anecdote that involves a girl having an accident while wearing a fursuit.
One reason could be that she is too young to be potty - trained. Babies and young toddlers don't have the control over their bowel movements yet. So it's normal for them to poop in diapers.
Once there was a little girl named Lily. She was out playing in the park all day. She drank a lot of juice and ate some fruits. As the day went on, she started feeling a strange pressure in her tummy. But she was having so much fun that she ignored it. Eventually, she couldn't hold it anymore and pooped in her diaper. She felt a bit embarrassed when she realized what had happened. Her mother quickly took her to the restroom to clean her up.
No, it's not appropriate. Writing about such potentially embarrassing and inappropriate situations in a fanfic can make people uncomfortable and may cross the boundaries of good taste and respect for others.
Avoid using overly graphic language. Instead of going into the gory details, you can imply what's happening. You could also add in elements of how the classmates respond with kindness and understanding rather than just shock or ridicule. For instance, one classmate could offer her a jacket to tie around her waist while she tries to deal with the situation.