What I do is, I go to my shared folder (the one called 'Public') in a file browser, right-click on the file I want to link and in the context menu that pops up I can pick "copy public link".
If that doesn't work, maybe you can figure out your user ID somehow and then create the link manually.
I have Dropbox version 2.10.3. I don't remember when I signed up for it though.