Hello! Sorry you're having such a rough time - and sorry nobody has replied to you until now!
Number one: Please ring your midwife / health visitor about how you are feeling. They will be able to offer you support and advice.
Different babies feed differently, but they all feed A LOT when they are little. My baby was tongue tied and it wasn't diagnosed till he was 7 weeks old, so my boobs got in a massive state and I ended up having to express and then feed him with a bottle for weeks on end. It was knackering and horrible and I felt like I was literally never sleeping.
It did get better.
I also refused to give up breastfeeding. I bf exclusively until he was 9 months, when I introduced a single formula feed in the afternoon to enable me to pick up some more work. My son is now 14 months old and still bf once a day. I am really glad I did it. However, please don't feel like you have to press on regardless. Keep reviewing the situation - think: ok, I'm going to feed him exclusively till the end of this week, then I'll consider my options again. If at the end of each week, you want to carry on bf, then great! If you decide you want to introduce some formula, then that's also great! I reached that point - it was what enabled me to continue breastfeeding the rest of the time!
You will probably be feeling bad too because you aren't getting solid amounts of sleep. I expect someone has already told you that sleep deprivation is a form of torture, but I'm just going to remind you of that, because it is HORRID! Please sleep when you can. If you need help with the housework because you haven't got time to sleep and look after the baby and do everything else, then ask for it. Or just leave the house be for a few weeks (if you can cope with that!). The important thing is a) you feed your baby and b) you get some sleep.
I bought myself a cheap gadget called a 'gimble' from Waterstones, which holds open a book so that you can read no-handed. I read a hell of a lot of books in the first few months of breastfeeding! Turning the pages is a bit awkward but you get used to it. I know people who read a Kindle while breastfeeding and said it was great - but I wasn't sure about holding a wifi device so close to a baby for hours on end.
For night feeding, I used to download podcasts onto my iPod and play them through headphones so that I didn't wake my husband up. I remember feeling verrrrrrrrrrrry sleepy through some of the science ones though! Comedy worked a lot better for me.
I think the biggest thing is to talk to people. Your partner, your family, your friends, your health professionals. You have a four-week-old baby, who you are keeping alive purely through your own milk production! How amazing is that! No wonder you're knackered!!!!
Hugs xx