Landlord Is Ordering Packages For Herself Using My Name

Location: Alaska

I apologize for the throw away account but I feel very uncomfortable and bugged out by this situation.

History/context: my husband and I moved into this apartment about 6 weeks ago with our child. Landlord insisted on me skipping the application and background/credit check and only going off of my husband's because I'm a stay at home mom, so I just skipped straight to signing the lease without the application part.

I received an email two days ago from a clothing website (a legit website) with a confirmation for an order that was about $120. I have never seen or used this website before. In the shipping details, my full legal/government name is listed along with my email and my phone number. However, the address and the billing address are both listed as her address. As far as billing information, it only shows up as "credit card". I have been religiously checking my bank statements and my credit statements and there's nothing out of the ordinary that I can see. I'm nervous on confronting her right away as she knows my husband is out of state for work for the next several weeks.

Do I file a police report? Should I confront her? Has anyone ever been in this type of situation before? What kind of scam could this be? I feel extremely unsettled by this and why she would be ordering things for herself using my name and personal details. Any recommendations on how to move forward properly would be very much appreciated.