Challenging to change much without admin rights. You may be able to set some folder level permissions, but I would have to test to see what you can do without admin control.
There are lots of ways to secure data on a Mac, and by default (unless they have been changed) other non-admin users should not be able to see your data outside of a few, specific by-design public folders. Again, without admin control, it is challenging.
And...if an admin wants to abuse their power, they can snoop on anything. Are you trying to keep things private from an admin user, or other general (non-admin) users?