Don't give up!!! Well give it a few more days if you can hang in there.
Day 4, I went to pieces for similar reasons. It was a particular hard day as its when your hormones really kick in and its difficult to be rational about anything. It got better.
She hardly needs any milk at this stage. I wouldn't say to top up with formula, if you are managing to feed her because if you do, what will happen is her stomach will expand and you'll find it very difficult to satisfy her with breast milk alone. Formula and breast milk are very different consistencies.
I would disagree with everyone saying 'don't express' for a few reasons. Firstly at day 4, I was massively engorged and it made it even harder to get DS to latch. I had a lot of problems getting him to latch and he made me sore in the process. Expressing using an electric pump helped relieve that problem slightly. It also gave me a bit of a break when he'd mauled me and it became too painful to try and get him to latch. It depends on your individual circumstances, but it worked for me.
Unfortunately I didn't manage to get him to breastfeed straight away. I never did properly get to the bottom of it, though a HV and doctor said he had very slight tongue tie - but only after two midwives and a paediatrician said he didn't. He also has a high palate which I believe makes it more difficult. My point being that tongue tie can be hard to spot, so if you continue to have problem seek a second (or indeed third) opinion as to why you are having problems.
In my case, DS's latch remained poor, and I ended up expressing long term. Then at 16 weeks something clicked. He started being able to feed without giving me pain. I'm led to believe that whilst this is unusual its not unique. He simply learnt and the physical problems he had seemed to resolve themselves as he grew.
I appreciate this is the extreme end of the scale, but it does illustrate the point about it not being straight forward and easy as you'd think and that perseverance can pay off.
Where you are now, I'm sure your emotions are all over the place and you are suffering from lack of sleep and it may well seem impossible. Hang in there if you can. But if you can't, whilst your emotions might tell you differently now, its not the end of the world if it doesn't work out for you. Be kind to yourself, and good luck.