I think I lit my cat on fire
Why do you think you lit your cat on fire?
Its fur was all singed and she was lying there writhing in pain
Lighting your pet on fire is one of the meanest things you could do to a pet. If you have the urge to do something so lousy to an animal, then you probably are not meant to have your own pet.
I was drunk at the time, I don't remember what happened.
Using drinking as an excuse for hurting a pet is horrible. Do you not love your cat? If you think you have a serious issue with alcohol it might be a good idea to get help for your drinking you could wind up hurting yourself.