Is it normal to blame yourself?

My daughter died from Sids a month ago. Deep down I know there was nothing I could do, but I can't help but blame myself as her mother. I was supposed to protect her but I couldn't. Everything I do I feel guilty about it. If I watch a movie I feel guilty because I'm not thinking about her during that time. I keep having morbid dreams about her. I am the one that found her and I am the one that did CPR on her so I keep feeling like she blames me. And I think that she won't need me anymore when I get to heaven because she has God now and he more powerful than me. I don't even know if this makes any sense, I just need help dealing with this.