Reaching in her sleep?

My daughter is 3 weeks old and will not sleep unless I'm near. If I'm too far out of reaching distance she will scream. I've also notice that she's be sleep and begin reaching her arms like she's trying to grab me.. and begin to scream if she fails to feel me. Even if I do hold onto her hands or take her hands and put them on me she'll scream until I pick her up. Has anyone else dealt with this? Is this normal??