Son won't sleep!

Cassidy 💜 • Mommy to a beautiful 1 year old!
My son is a month old, he's starting to wake up in the middle of the night and just not go back to sleep. He woke up at 1am, didn't go to sleep until 7am. He was dry, fed, I rocked him. Even tried to put him in the swing but he didn't want any part of it. He would doze off and wake up 5 minutes later. I'm getting no sleep whatsoever and I'm honestly over it. It's hard not to get frustrated, but when you're running on literally 2 hours of sleep, it gets the best of you. Any advice on what I can do?
(Please don't say 'sleep when  he sleeps'. I can't sleep during the day; not because I'm busy, but because I've never been able to sleep during the day, regardless of how tired I am)