my 5 week old ds2 is exactly like this. his older brother was similar (also a 10lbs 5 giant at birth).
Most babies are fussy in the evenings. It can take me hours to settle ds2. Last night it was three hours of holding, feeding, burping, feeding, jiggling, carrying, tummy rubbing, feeding, wtf is wrong with you etc. It drives me bonkers when I just want sleep more than anything.
my eyelids were drooping but he was wide awake and grumpy.
It will pass. Nearer ten or twelve weeks they stay awake longer in the day more and sleep longer at night (though ds1 never managed more than 3 hours until he was 7 months. He is a brilliant sleeper now though. There is hope).
I think babies don't start producing the melatonin to regulate their days and nights until around 12 weeks. The fussy grumpiness is probably just tiredness and the baby's utter inexperience in dealing with it. They just don't know that sleep will fix it.
If ds1 is anything to go by, the nights will be hard fur a few more months BUT he will become more fun to be around in the day. The smiles and the gurgly laughs will make you so happy. You will still get his fussy moments but not so often.
hang in there. And get dh to take him from you when he can, out for a walk so you can't hear him, preferably. Keep expressed milk in the fridge for him.
- so you can get longer chunks of sleep than the 90 minutes currently. 4 hours continuous sleep minimum is what you need to stay sane.
- so dh learns his own techniques to settle a grumpy baby. If he doesn't, he'll not have the confidence to try later and will always hand the fussy infant to you.