People trotting out the old "men need time off" line, the baby is only 5 weeks and has reflux ffs! When does OP get a break?
OP YANBU, would write off this morning, but you could to have a talk (another day) with DH about division of childcare at night / mornings / weekends and how to make sure you both get roughly equal time for yourselves. With something like reflux - if the baby is up a lot in the night - you will both need to do nights, or it will break you. He may say that he works, but that doesn't mean you should have to do all the nightwork.
New baby is tricky, after our first we found it v hard to adjust to having much less time for ourselves as individuals, took DH a while to realise that it wasn't OK for him to go out after work for drinks, nice spontaneous social evenings, while I was stuck at home, in pain from the birth and awkardness of new breastfeeding, sleep-deprived, weeping and in despair with a colicky baby screaming for hours on end! DC2 was easier, we had our teamwork more sussed by then!
DH and I (2 DC, terrible sleepers, I do almost all nights) have a rule that any hangover lie-ins must be negotiated and prescheduled! Otherwise it's up and get on with it, unless we are feeling generous and take pity.