Can someone use my IP address?

[Alyssa]

I recently found out that the oldest daughter of my mother's boyfriend is being harassed via social networking sites. She took her computer to a computer specialist and he or she traced the IP address AND my Twitter account. I am the only one with access to my laptop but, even if I had a reason to harass this woman, I wouldn't, so how is it possible that everything came back to my IP address and Twitter?
I've only said what was told to me. My mom texted me and accused me of harassing her boyfriend's oldest daughter via social networking sites.

She told me that the daughter took her computer to a specialist who traced all of the messages back to my IP address.