Can't remember this book

[adastrum]

Hello! So, like everyone here I read a book back when I was younger and I can't for the life of me remember it's name. It was either a fantasy or YA novel. The book cover was red and black, I think it had the outline of a wolf in red or black. Anyways, the plot was basically about this young princess who was feared by all the servants, and kingdom because she turned into a monster, I think it was a wolf, once a month. I think she either had a red cloak that prevented the transformation or a potion or she was just locked in a room until the transformation ended. I can't quite remember. Anyways, one day her father says she's been betrothed to some prince from an island. Now this prince and the island kingdom are feared because he's supposedly evil and violent. She also has brothers who are protective of her, and love her. So anyways, she forced to depart, but she's very self-loathing so she feels she deserves to be married to a monster since she is one. Turns out the prince and the kingdom aren't nearly as bad as she expected, they fall in love and I can't remember if the brothers try to rescue her or something. Anyways, it was an incredible book about learning to love yourself, and a lovely romance, and I would love to read it again. Please let me know if you know the title, thank you!