bought a book on amazon today, not downloaded to kindle library
Not enough details.
What device and/or app are you using? Was the transaction completed (it's not 'pending')? Does the title show in 'Content and Devices' of your Amazon account? If so, are you able to deliver it (using Actions (...)) to the desired device (or is it missing or grayed out)? Is the title formatted to be compatible with the desired device (does the product page list availability)?