Facebook saves everything you look at, like, comment on, share, post and search and anyone that actually has access to your account other than you can see everything you are doing on FB. All of this is stored in your Activity Log. You can get there from your Home Page or your Main Front page, just look at the images below.
Here's the bottom line. Ensure you go to your overall FB privacy settings and set-up how your want to secure your page initially. Know who your friends are. Change your password every quarter. Don't believe or act on everything you read or see on Facebook without checking it out and finally, stay on top of your activity log, it's as simple as that. Click on the links to see information and instruction pertaining to your Activity Log, straight from Facebook. ACTIVITY LOG / DELETE ACTIVITY LOG SEARCHES