You are a curious mom and you got a fussy baby.ok firstly by your history as baby is having weight well and passing urine and stool nicely but since the child gets so irritated then an ear examination and an ultrasound abdomen would not harm the child .Breast milk is a natural soother to child so putting the child to breast tends to solve the irritability issue but leaves the mother exhausted.that is what is happening with you .
So
1.plot the child's growth on a growth chart and see if the baby is doing well.
2.get the tests done as I have just mentioned
3.you yourself should sleep when the baby sleeps that will give you some relaxation.
4. Get your feeding technique checked ,there are videos on you tube from Australian breastfeeding association ,please see them.
5.babies settle by 12 weeks with their night schedule.
Next Steps
try colic hold for crying or turning TV at zero channel ie: the buzzing sound .try it you are the best judge.best of luck😙😰