I would avoid using songs from Into the Woods because that is a legit show. As far as Jekyll & Hyde goes, I don't really think that the songs fit high school age characters. I've only seen HSM once, and it was the stage show, which I am under the impression is almost the same as the movie, so I may not be the best judge of what's right and wrong. I played the "other" girl in J&H, Emma. Most of Emma's songs are duets and her solo wouldn't fit HSM, and I don't think that any of the lyrics really fit Gabriella anyway. Even though Lucy is a prostitute you might be able to get away with "Someone Like You" (a beautiful ballad). It is in a book for young women/teens with alternate lyrics. If you pick it and it's the show version, I think you should start with the second verse and sing it through to the end.
As long as you choose something with a pop sound and stay away from legit songs you should be fine. Just think about how the lyrics or character parallels the one that you are going for.
Currently~ Miss Myrna Thorn in Ruthless! the Musical
Recently~ Emma Carew (Jekyll & Hyde), Sister Mary Leo (Nunsense), Demeter (Cats), Tzeitel (Fiddler on the Roof)