It sounds like I am going to hand you a list of tried and true tips about how to get your colicky baby to sleep but that's not the case, so now you've been warned ahead of time to go look on Baby.com or something like that for that kind of information.
My own baby has grown up into a 6 year old kid who goes to bed at a reasonable hour and has slept through the night for many blessed years. I know, I hated people who said that about their kids when my kid was up every hour and a half, too. When the little man was a baby, he had periods when he could not be tamed. Anyone who was around at that time knows this is an understatement. Suffice to say I really felt like I tried everything I could to soothe him but sometimes all I could do was either hold him close or to let him scream for a bit. (I tried not eating chocolate, garlic or broccoli, I tried switching detergents, I tried the swing, I tried soft lighting, I tried walks, singing, in the sling, in the Ergo, I exhausted my fatigued brain trying to prepare for what would inevitably be a long night.) As he got older, sometimes there was a window I could reach where sleep would come effortlessly to him but if I missed the window, the very fabric of our house would unravel into hours of, well, it would be another long night.
It's not about the baby, though. It's about knowing when you are the overtired baby and the ability to decipher when you're dealing with one so you don't try to have a rational conversation. My point is, there are plenty of people who look like adults who are actually overtired babies who just need to scream or just need to be held.
Case in point, last night. I had been up at 5am the morning before to the cheerful sounds of the fire alarm telling me they needed new batteries in that subtle, fire alarm way they have. It was a fine day. Nothing weird or terrible happened but when I tried to go to sleep, I found I had missed that sweet spot, the sleep window that I had so desperately needed was beyond rational help. Maybe it was the laundry detergent, maybe it was the moon. Maybe it was the chocolate, the garlic, the hangover from the election. I had to just lay there for 5 minutes and let myself 1) be held and 2) sob. No one needed to sing Baby Beluga to me this time, but I am not ruling it out. It's nice to have people in my life who will hold me so close when I need it or who will give me the space needed to grind my own gears to a halt.
Anyway, that's today's secret for calming an overtired baby. It worked for me.