Baby sleep patterns must be one of the most searches topics on Google. Even I used to search everywhere and wonder how this thing is going to resolve.
But the simple answer to this is “patience”.
Babies have very tiny stomachs and to create a schedule for them so that you can sleep is not correct.
I would agree feeding them every 2-3 hours is essential. But you can’t expect them to sleep at night.
They will stay awake at night for 3-4 months and then things will get better, they will understand the difference between day and night. They will wake up only 1-2 times for feed.
Meanwhile you just have to sleep when the baby sleeps; this is your only mantra. I think acceptance is better than trying. During the night they cry due to two reasons, one they want to play and they are craving for your attention. While you’re busy trying to make them sleep.
Second it must be colic, they develop these gas pains. My baby was a colic child and nothing used to help her till I gave her colic drops called “Colicaid”. Few drops and then the gas would pass out. They will feel much better.
Remedies for colic, here.