Separation anxiety?

My little girl is almost 9 months and for the past few weeks she will not let me or my sister (she watches her while I work) put her down. She won't play by herself anymore and doesn't want other people to hold her. I'm so hoping this is a phase because I am exhausted and it's easier to just pick her up than hear the bloody murder screams that come out of her mouth. Suggestions? Anyone else having this issue? I read that it could be separation anxiety, and people say I'm spoiling her and that's why she does this... but all I do is care for her and play with her- I don't think that's spoiling a little one 😢