How Do I Block Somebody From Facebook?

About six months ago I was walking down my street and noticed a gorgeous mural that had just been painted. My neighborhood is kind of dismal and this mural really brightened up the area. The mural was signed and I thought I should write this artist a note to thank her for making our neighborhood look nice. She was very easy to find on Facebook and so I wrote her a message. She never responded and I quickly forgot about her. Within about a week I started noticing these strange subject lines in my email inbox. "Do you know Lecinda Akerson? or Muhammed Bornstein" All these people I never heard of. I don't know what this woman did but every time I go to my Facebook page I find all these people's pictures and comments that I don't know. I know Facebook connects people but I don't know any of these people and I don't want to. Apparently this woman connected her Facebook account to mine in some fashion.. I don't know. I'm 85% Facebook illiterate. As I stated my only purpose to sign up was for people to find me.. Is there some where I can disconnect all references to this person? What can I do? Should I just close my account and start a new one? Any suggestions would be appreciated.