That sounds amazing! Sounds like you have a good direction for the story, and I'm liking the imaginary friend angle. You are welcome to do whatever your mind and inspiration lead you to do! Here are my thoughts:

The meat of the story seems like it'll happen when she's ADA, as far as I can see. Her backstory sounds really compelling, but because her childhood and escape and her life on the streets are really more character development than actual story, you might be able to introduce them in short flashbacks when they become relevant. Flashbacks are best delivered when readers know they want them, so it might be cool to have the name she adopted on the streets come back to haunt her in the story, just when things are really getting intense, and someone she cares about (the sheriff guy?) finds out about her past on the streets or is endangered because of it. Making her past relevant in the now of the story would be great reason to delve into your protagonist's experiences as a child and teen!

Having her confess some of her experiences to someone she is becoming close to would also do double(triple?) duty as important exposition and character/relationship development!

The thing is, it's really tough NOT to write the interesting backstory! I have scenes upon scenes written of backstory for main and side characters for various stories, and most of them will never see the light of day. But it's really enjoyable to write them, and these contest rounds (like today's!) are excellent opportunity to get the words out of you and onto paper.

If you find that her past simply can't be alluded to by other characters or shown in her lingering fears and traumas, that's cool. Go with your gut. You know what you want to write, and if you decide you want to change things up later, that's why it's called a first draft! You don't have to commit to one thing for good.

Best of luck!