Pack and play

Does anyone’s baby sleep in a pack and play in their room? Does a crib mattress fit in a pack and play? I bed share with my son and he’s been constantly moving around in his sleep and I haven’t been able to sleep because of it. And he crawled right off my bed and hit his head this morning right when he woke up. (Called doctor everything is good) but anyway I want him in my room still but just can’t do the bed sharing anymore because it’s getting dangerous. So just wanted to see if anyone else’s baby sleeps in a pack and play in their room? If the mattress doesn’t fit I’ll just move his crib in my room