Is this normal ?!

I think what you are referring to is mainly separation anxiety. Or if you've always made a habit of picking her up every time she cries or fusses then she'll continue to do that and get worse and worse, which is different from separation anxiety. If it is you picking her up every time, you've trained her that she needs to cry or fuss to get her way. I've got a four month old who, if I know she's changed and burped and fed and not tired, I will not pick up if she's crying. When she stops crying and has been happy for a few minutes I go over and play with her and pick her up etc. This reinforces to her that she needs to be happy for Momma to play with her. If it's the separation anxiety, there's not a whole lot to really do with that. A lot of kids go through that, and personally I just wouldn't pay a whole ton of attention to it. If you pick them up all the time in response to it, they'll do what I described above. I would just say try and talk and sing to them from wherever you are so that they know you are still near even if not right in front of them. I hope that helps ;)