Baby frustrated and sucking her hand raw

I looked up this forum because I can post a question here without becoming a member. I'm not planning to join, but I have a burning question. My daughter is almost 6 months old and has been sucking on her right hand very frustratedly for about 2 months now. It's completely raw and broken by now, but she keeps sucking on it. If I take her hand out of her mouth, she gets furious. It's like an obsession; she has to suck, otherwise she gets incredibly angry and frustrated. I gave her a teether and other toys she can safely chew on, but she just throws them away. She has that hand in her mouth all day. A week ago, I started introducing solid foods using the Baby-Led Weaning method, hoping she'd be content if she could chew on food for 1 or 2 times a day to let off steam, and she loves it, but in between, she's still chewing on her hand. How can I help her stop this, and why is she doing it in the first place?