I have a book showing up on my bookshelf, but not my public bookshelf....  I physically have the book, so it hasn't already been ordered.  Why doesn't it show on the public shelf??

which book?  It's not on individual or one hour buyer's remorse hold?

Check to see if it's on a Wish List Hold. When I first joined this site, the first book I posted was Wishlisted. I didn't realize that at first and kept trying to repost it to make it show on my Bookshelf. Finally I caught on (luckily, well within the time to agree to send the book out), and earned my first credit.

It's probably on individual book hold, as Mary mentioned.  If it is, when you look at your shelf you'll see a red crossed out circle on the green check to the book image's left - if it's not on individual hold there's only the green check.  If it's on Wish List or Buyer's remorse hold, there'll be a grey exclamation mark all the way to the right, and if you put your cursor over it it'll tell you which it is.  Was this a book you received from PBS?  The system automatically puts received books on your shelf on hold unless you mark otherwise when you receive it.  I often forget to uncheck that box when filling out the survey and I'll find books on my shelf that I didn't mean to repost.