I gave my sister my SSN

So when I first turned 18, my older sister came to me and asked me if she could use my SSN to open up a light bill. She was a single mom with two kids at the time and was really struggling, and I felt sorta obligated to help. I really love my niece and nephew and when she told me they couldn’t even watch TV I felt so bad. She made me promise not to tell my mom and swore it’d be temporary and that she wouldn’t miss a payment because she knows how important credit is.
At the time, I didn’t really know myself and wasn’t too worried because I knew I wasn’t getting my own place anytime soon (I was just starting college). She ended up lying and let the bill go over thousands of dollars without me knowing because I was under the impression she was always paying it. Once I found out, I called and had them close the account so she wouldn’t make it go higher. Now she’s refusing to pay it and I don’t know what to do.. I spoke to the company and they sent me identity theft/fraud paperwork to fill out. She says she won’t get in trouble and it’s not fraud since I told her it was OK. But some people are telling me permission or not, it’s a crime. I just wanted to know what I should do? I don’t really have adults around me for guidance or advice