1 Book Found

Based on your description:

"YA standalone fantasy book from before 2010 where a girl grows up ostracized for her garish looks. She eventurally gets to chance to live and work at the castle and navigates a space where looks are even more important. She eventually meets an elf who shares that her hair color is a blue so dark that humans can’t see it, meaning she has some elf heritage. She travels to the mountains to learn more and ends up staying in a mountain with more elves. On the journey the traveling party gets attacked by orcs. There are healing waters in the caves and a market within the mountain. She slowly begins having feelings for the prince. She gets manipulated by a beautiful woman in the castle to use magic to alter her appearance, giving up her beautiful singing voice that is also due to her elf heritage. The magic comes from a magic mirror that she becomes trapped in."