Threatened with International Lawsuit

I live in the United States, and there's someone I've known for several years inside Spain that we've recently been through a huge fight. After telling them to never contact me again, they have repeatedly ignored this request, and has even gone so far as to stalk my social media. I made a post about them on social media, which didn't mention them by name or any other means, but they then messaged me on another social media account and began harassing me. I took a screenshot of the messages and posted them on the initial social media site, and they have told me now to delete the post because I posted it without their consent, and that they started a police report and gave them all of my information (full name, phone number, email address, home address, social media accounts) and that if I ever post anything about them again, they will continue with the lawsuit. I don't intend on ever posting about them again, with the exception of this thread asking for advice.

Is this legal? Do I have anything I need to worry about? I have tried several times to cut off all communication with this person, but I am now resorting to unfortunately deleting all known information she has of me (social media accounts, changing phone number, etc) in order to cut off contact.