Not to worry. Just take action. Stop using the faulty outlet immediately. Inform the landlord and insist they bring in a licensed electrician to correct the problem.Okay thank you for the detailed reply and assistance, much appreciated. I will get a tester and see what I find out. I hope I don't find out that it's a major issue.
That said, it's often a very simple fix, and doesn't necessarily require an electrical license. Many outlets are simply miswired at the wall box, which is easily corrected with some basic electrical knowledge and handtools.