My personal experience, hope it helps.
I used to hurt myself by punching walls. Brick walls, concrete walls, wooden walls, it didn't matter. Other people I knew in high school or, later, in college, would burn themselves or cut themselves. There were always different reasons behind it: some people actually thought it was "cool", some people did it to express (or hide) from their emotions, some as a call for help, and some of us didn't know why we did it.
I hurt myself (and a good number of walls) because I couldn't think of another way to express my anger and sadness when my stepfather beat my mom and it later became the way I dealt with anger. No one noticed for six years and, even then, no one made any attempt to stop me.
In college, I finally started going to therapy and that helped some. I was urged to find new ways to express my frustrations and emotions--I tried writing poetry, talking with friends, exercise. Some worked, some didn't. When I feel upset, I hop on my bike and go for a grueling ride; it reminds me that I *can* feel happy again. The important thing was trying different things to deal with the emotions that made me want to hurt myself and finding the right fit for me. A friend in college who cut herself was able to stop by calling a close friend every time she wanted to hurt herself; they'd have a long phone conversation or go for a walk to do something together.
As a result of hitting walls, I've permanently damaged my right wrist and hand. Sometimes, I feel overwhelmed and I still want to hit things and I would lie if I said I no longer hurt my wrist hitting walls. Self-abuse is a hard habit to break.
So all that said, it's important to make sure your daughter knows you love her and that you're trying to help her. Maybe you and her therapist can work to figure out if there's a specific reason behind her burning herself. If therapy isn't working on this issue, consider trying another counselor; some people react much better to different therapists. Let her know that you know what she's doing and you can't be deceived by her claims that a lighter got dropped on her. Be loving and supportive and hang in there. She's lucky to have a mom who's trying so hard to help her.