I did not previously have my book, but I took possession of it.
3. I have got my book.
The book is currently in my possession.
Sentences 1 and 3 are basically the same. Read this explanation that Ola wrote to answer a similar question.
She explains that have and have got have the same basic meaning, but the first is more common in American English and the second is more common in British English.
As a Native American English speaker, I would NOT normally say, "I have got my book."
I might say, "I've got my book" or "I have my book."
