Yeah its pretty normal for babies to be clingy because they are coming to terms with the fact that they are an individual person as opposed to be being part of another person (ie in the womb).
Try playing games like peek a boo or hide and seek with your baby. Might sound silly but games like these will help baby learn to "miss" you when you're gone but also reassure them that baby will never be alone and that mommy (or anyone else close) will always come back and be there for baby.
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