sleeping on belly 😳

Pa
So my LO is 3 months and one week old and has been super fussy in the middle of the night for the past week or so. 
Typically we put him in a swaddle sleep sack with arms tucked in. I've slowly been trying to bring arms out by leaving one unswaddled when tolerated and tonight he was so upset and uncomfortable for so long and I tried a ton of different things to try and get him comfortable and be able to set him down but the moment I would his eyes would fly open and he'd throw his legs in the air and start crying and rolling side to side. I finally tried untucking both arms and just wrapped the wings of the sleep sack around his body. Well within minutes he goes and flips himself on his belly! He's been out sleeping well ever since. I don't know if I should leave him or flip him back over... I read that if they can flip themselves over after you've placed them down on their back you can leave them but I'm so paranoid and not sleeping still because I'm worried about something happening to him. Meanwhile my fiancée is right next to me snoring away, oblivious 🙄 just curious what other mommas thought 
Edit to add he is sleeping in our room still, near me. 

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