I believe there were four or five books in the series, maybe more or less. I remember the protagonist being female. I read this approximately three years ago, and I think it was relatively new then, but maybe not. The cover art seemed more modern to me. I don't remember any of the names in the story.
I believe that the story went something along the lines of an elf baby was left in the human world, was adopted, and then, due to some sort of magical fire, I believe, was discovered and led back to the elf realm.
I remember that she was taken in by a couple who owned a magical beast ranch, and the protagonist had to attend some sort of magic school. I vividly remember that the protagonist didn't really ever "power up" to defeat the bad guys in the first one or two books, and that it made me kind of mad. I believe she got a lot more powerful towards the later books.
If there is anything you think I should add to help the search, feel no hesitation to tell me.