Please can someone give me advice

Have you tried formula (if you're breastfeeding?) There are some that help with preventing reflux etc.
As for sleep, my LG is 6 months and still contact naps and its the only way she sleeps. I know thats not for everyone and also not possible for some but I do it as it gets her to sleep and for me that works. Can you just do contact naps rather than putting her down? 4 weeks is still so young so she probably still just needs to feel close.
It does get easier eventually but you're in the trenches at the moment and it sucks. Do you have a partner or family nearby? Someone that can hold her so you can have a cup of tea or a nap or a shower?

Firstly I think you need to have a look at postpartum rage, it's very very common and very normal and perhaps speak to your GP about it to see if they can help you. I think there's also a few other things going on here. If you are EBF it's very normal to feel "touched out" because you've got a baby attached to you at all times and going onto formula or combi feeding may help relieve some pressure. Another thing is that it's super normal to feel overwhelmed by this new way of life, let yourself grieve who you used to be, it doesn't make you a bad mum just because you miss the person you once were you're just growing and shifting into a new version of you. Becoming a mum is the biggest metamorphosis a woman can go through. I know right now it might seem like this is forever, the sleepless nights the hard days, but it's been 4 weeks. Things will change so fast. My LG is now 5 months and I feel like I blinked and missed it all. You won't be in this place forever.

I definitely feel like you should reach out to your health visitor before you’re 6-8 week review.
The way you have described your baby could be post partum rage, depression.

At 4 weeks old your baby is naturally going to be dependent on you and this is something I think a lot of new parents do not anticipate until they are in it.

You haven’t said how you feed baby? Breast or formula? If baby is vomiting after each feed / have you accessed GP to discuss colic or reflux?
Is baby rooting after an hour each feed?
Do you leave the house and get air? Cabin fever is very real and the days can roll into one and feel like you are on a loop.

Do you get any respite / any opportunities to sleep or eat etc.

If she’s throwing everything up then could be reflux? What are nappies like etc x

Oh I'm so sorry. Like everyone has said, you should probably talk to your GP or health visitor about the baby throwing up and also about how you're feeling. Do you have anyone helping you? If you can, getting someone else to hold the baby while you leave the room or the house might be a lifesaver. Do remember that if the baby is safe and clean, you can put her down and let her cry while you take a few minutes.

Most of all, this is only 4 weeks in. It's not gonna be like this forever. I know it feels like eternity and I don't mean to minimise how you're feeling - even a few days is a long time to feel like this! - but there is help to be had and time will change the situation.

I agree with the above - it really is such a massive adjustment and although people tell you how hard it is - they don’t tell you why it’s so hard and it really isn’t something you can plan ahead of time. My LO is 10 weeks old and I really struggled with the lack of sleep which had carried over from my induction and labour and also the physical pain and discomfort from the whole experience at first.

If you have support from a partner, family or friends I’d definitely lean on that more - I’m bad at asking for help but I’ve just had to especially with my partner with the chores. And sometimes when I can’t settle her I just tell him I have to tap out.

Things definitely hit a positive turning point at 6 weeks and you’re so close to that so honestly just be kind to yourself and patient in the circumstances and it will get easier.

If you can get a baby carrier so the baby can settle on you but you can move around and still be mobile then I’d really recommend that. Check out Vinted!

I'm sorry you feel this way. I can certainly relate to that. I was exactly like you 3 months ago. I went to a pp depression mostly because of motherhood adjustment, painful episiotomy scar, multiple infections due to catheter and also unsuccessful breastfeeding...
I was surviving. I overcame really because of the support of my husband, patience and taking a Break out of town. Baby is now over 3 months and my experience is so different.

Give yourself a little break. Find someone who can help you with the feed and take care of her while you are sleeping. Even 2 hours will be a life saving for you. The sleep deprivation is the hardest part I think.

Surround yourself of Mamas and experience mother. I went to all kind of breastfeeding café. This has helped. Talking about your issues with someone helps to have perspective and feel human.

Don't be too hard on yourself. I felt very guilty of everything but the best thing is don't do that. Take as much help as you need.

Are you breastfeeding or formula feeding? Are you keeping her upright after a feed and burping her? If bottle feeding is it possible the teat size flow is too much etc?

Throwing up after a feed could possibly be reflux.

As baby is only 4 weeks old she's still technically adjusting to being outside of the womb and it's going to take time and patience before you both settle into a routine. You could try using a dummy to settle her in a bouncer or swing if you have one, playing nursery rhymes in the background or putting on Hey Bear baby sensory on YouTube worked wonders when my boy was newborn and gave me some respite to shower and have a hot drink.

If it gets too much put the baby down safely and go into another room and allow yourself a few minutes to calm down and gather yourself. Hope it all improves for you soon.