Hi Ameliesmumvic, I have only been a mum for 8 weeks (today!) so I don't feel like too much of an expert yet but your experience sounds much the same as mine.
DD was a very windy newborn and we started using Infacol which really helped.
Are you swaddling your DC? That also helped us. DD seemed to hate it but actually sleeps much better swaddled.
We had problems with DD's latch and I think she was falling asleep before getting enough milk. Two things really helped me: I saw a BF counsellor at a baby cafe (I think they run all over the UK) and posting on Breast & Bottle Feeding. I got great advice and support there.
I think DD was about 3 weeks when I first posted on here out of desperation! It does get easier.
We started a bedtime routine early on too - nothing rigid - feed, bath, massage, last feed in a quiet room and settled to bed. This really helped DD to sleep longer too.
I think at 3 weeks nightime waking, BF problems and wind are all common and they do pass. I haven't used infacol on DD for a couple of weeks now, she'll regularly do a 5 hour stretch of sleep at nught before waking to feed and BF is going well.
I know how horrible it is having such little sleep and I think you're doing well to post on here after 45 mins sleep! Hang in there, it does get better! x