If I use firefly and save to library are my images private? How do I retrieve them?

Please see my response in this message for the various ways images can be saved:

https://community.adobe.com/t5/adobe-firefly-discussions/where-would-i-find-previous-images-i-have-generated/m-p/14355007#M5082

Among these ways of saving images, there are two types of saving. One way is the actual image file itself. That is what is downloaded locally or to your Creative Cloud library.

The second way is saving the data (prompt, mode, styles, and seeds) which can regenerate the exact image again. That is what favouriting or sharing a URL does. If that URL is shared with others, they can generate the image again, just as you can. [You do not deal with the URL directly in "favouriting", information is stored in your local browser for you.]

So, if you are saving a "favourite" or "share a link" and if you do not want anyone else to see the image, you have to protect them from getting that URL. On the other hand, if you want others to access the image, you can provide the URL and they can regenerate it just like you can.

You mentioned "save to library". That option saves to your Creative Cloud library and images saved there can be used by other Adobe apps and are only available to you by default.