Would love to hear people's thoughts or experiences

This may be a long one but I'd like to know people's thoughts or if they've experienced it as I'm finding support from the health visitors or midwives aren't really there.

My son is 1 month old, we breastfed for the first week however after 3 days we had to give him some formula too (cow and gate premade) as my milk weren't filling him up (no one told us that my milk wouldn't fill him, so we think he pretty much starved for 3 days :( ) he struggled to poo right from taking formula for the first time, he literally screams And pushes to go to the point he tires himself out from screaming he falls asleep. I then had to take antibiotics as I got am infection, the doctor told me I couldn't breastfeed, I didn't for about 5 days when I went back to get my stitches looked at, I told the midwife about his bowel movements and she said I could have breastfed and we tried to get my milk moving again but it had dried up to much :( (I was devastated and it really made me feel depressed because I felt It was my fault for him tummy problems then)

The midwives told us to use premade milk rather than powder to try help him poo, after a week and a half it was far to costly with the amount he has so we used the powder of the same formula. His bowel movements became worse and he started only going once, if that a day and really struggled again but he was only going once a day but became very windy. After another week on that we got told to try changing brand so we're now using sma powder.

We're finding he's still only pooing once a day and still really struggling to go (It's worse in morning at 4am-5am) we've found he seems to be having more milk as if he isn't filling up he's having around 60ml every hour and a half usually he would have 120ml.

So far his sleep routine is...

He has 120ml then will go bed at 7pm sleep till 10.30pm sometimes 11pm he'll have between 90-120ml then wakes again at 2.30am he'll then wake again at 3.30am to start trying to push his poo and stuff and he'll have another 90ml then at 5.30 he'll have another 90ml then again at 7am he'll wake and we get up he'll have another 90ml but split in 3 every 15min. He'll then fall asleep about 9 for an hour then he'll be awake till about 1.30 then he'll fall asleep for 45min then he'll sleep for 2 hours at about 3.30ish then wide awake again till 7 when we have to gently get him to sleep in between the gaps he'll have about 60-90ml of milk each time.

We're struggling to get him into a routine of sleeping and having enough milk, it feels like the milk isn't filling him up enough. I don't want to keep changing his milk because of his tummy and bowel movements.

My partner works from 4am till anywhere from 12 30pm- 3.30pm. So he gets up at 3 15am to get ready for work. So I take more of the night feeds as he's a lorry driver and has to sign to say he's had 8hrs sleep minimum but actually he's only getting about 5 hours if that.

Has anyone got any advice what we can do about his sleep routine, food and if anyone's had their baby struggle to poo so much :( we don't really know what to do but can't get hold of the health visitor for advice the doctor just says he's to young for anything and no one is giving advice on what could help.

We've given him warm baths, tummy massage, bum massage and cycling his legs and also cooled boiled water none of it helps with him going.

Sorry for the long message just I need some advice from people. We're struggling to get any sleep too :(

Thank you anyone who reads it lol xx