Perijee & Me by Ross Montgomery (author)
When 11-year-old Caitlin discovers a shrimp-like alien creature on the shores of her island home, she takes responsibility for teaching it about the world. Mostly, this just involved stopping little Perijee from eating everything! Caitlin becomes increasingly close to her alien friend, treating him like a brother. There's only one problem - Perijee won't stop growing. Then the authorities try to hunt him down and through his fear, Perijee disappears and starts causing trouble. Caitlin must leave home and travel across the country to try and convince Perijee to stop destroying everything before it's too late.