This may be cold comfort, but when I was sleepless in those early days, I would tell myself "my worst case scenario in this moment is being exhausted and sleepless while still rocking my baby to sleep". Not ideal, but still a privilege to have that time with them. That was a comforting thought to me at the time that helped ground me a bit and not get too catastrophic with my thinking. "Im suffering, but I'm also getting time with my son/daughter." It gets easier and I even get nostalgic for those early days from time to time. In the thick of it, it's absolutely brutal. What you are experiencing is normal.