Hey there, eli!
First of all, asking for the book is really nothing to be embarrassed about! So if you are out to your mom, it will be OK to ask her about it. Could you maybe just write down the author and title and give her the slip of paper and ask her for the book?
You may, of course, also be able to simply check it out at the library without your mom. Would that be an option? I would only go that route if your mom has difficulties accepting the fact you're trans really. If she is supportive, then asking her for the correct book will help her better understand what your needs are. It'll help you to support you better.