You can probably obtain information by looking at the browser cache. When the browser downloads pages, it stores copies of them in local files, so as to speed up operations if asked to inspect the same page again. Whether a specific page will be cached or not depends on what the server says about the page (there are HTTP headers for that); old pages are automatically removed from the cache so that its total size remains low; and the user has the possibility to "clear the cache" manually.
Location of the cache, and its internal format, depend on the browser type and version, and the operating system. If you use Chrome on Windows, this freeware utility purports to be able to let you see and navigate the cache contents (I have not tried it and I do not vouch for its quality). Alternatively, go have a look at the files in
[User Profile]\Local Settings\Application Data\Google\Chrome\User Data\Default\Cache where
[User Profile] is the home directory of your account on the machine (you may have to configure your file explorer to show hidden and system files).
Of course, if someone potentially evil and hostile could use your computer, then he could do a lot of bad things with it, including planting malware which will spy on you and siphon out the contents of all your files and passwords and secrets. However, if the said person used your computer to log on Facebook and left enough traces for you to see it, then chances are that he was not that competent or did not try very hard for concealment.