I'm worried about my little baby 😔

So my baby boy will be 1 month tomorrow which is technically is actually due date. He born a month earlier last month on July 23. He gets red all the time. Sometimes in his sleep. Today is his 5th day and still no poop yet. However he shows no signs of distress or in pain from constipation. Sometimes when I wake him up to feed he's too tired to even eat enough he rather sleeps but sometimes he would nurse for half an hour to s full hour. I do a lot of skin to skin. I cuddle him a lot but also give him space in his bed. I'm up nearly all night with only a couple of hours napping just to make sure he's okay and is breathing okay. Am I being paranoid? My bf seems to think so. I just wanna make sure I'm doing okay as a first time mommy. Please no harsh judgment 😞