I've got the idea of being in an adoption home for an entire childhood, where she never fits in etc, kids tease her etc but in a non-cliche way, then come 18 she leaves and trys to fit .. although I'm having difficulties trying to finish it well.. can anyone help?!
Honestly, that sounds very cliched. Yes, it's pretty much impossible to come up with an original idea, but the whole thing - kid who is teased and feels like she doesn't belong runs away - is extremely overused.
Your writing doesn't have to be centered around such an obvious example of belonging; my advice would be to make a mind map, or list, of all the smaller & less obvious examples. Look at your everyday life & try and find situations where you have felt either a sense of disconnection or connection with others or the broader world. It can be anything and everything - e.g. traveling alone on the train. What is the social protocol? Everyone sits there, maintaining a certain distance, avoiding eye contact etc etc. What does this say about our society and how does it demonstrate belonging? The avoidance of personal contact seems to suggest an unwillingness to form connections, a disinterest and isolation. Yet this ritual and social norm connects them, binds them in a way.
You can find examples of belonging and not belonging in absolutely everything. Your writing doesn't have to be all action and drama; it can be something incredibly simple. And by really getting involved in the characters thought process you can create movement and development.
Anyway, I hope it all goes well!
EDIT: I just realised she doesn't "run away", but leaves. Still, I don't think that really makes a difference in regards to what I've written.