I don't want the usual young teenager mother drama, but something different. Any such drama? Like either a teenager befriends a young homeless girl or the girl is always "hiding" out on the streets because her parents are troubled, or if she's a young teenage mother, she only focuses on the kid and isn't the least interested in romances or similar. 

Like it's a true story of a girl who's too young to be a mother and a little girl.

Not a drama, but a movie comes to mind: Kid Mon

Still not maybe exactly what you're looking for, but has the teenagers taking care of a neglected kid.