I spent most of day 3 crying too, it's completely normal, don't worry. My little one is three weeks old today and I've had a few days so far where I've not been able to stop crying, and felt totally inadequate. I also didn't want to burden my DP with it because he's working his ass off for us, but he keeps telling me that is his job, and he can't help if he doesn't know what's going on with me. So now I'm trying to make sure I'm more up front with him about how I'm feeling.
If you want to switch to formula feeding, then do that, it's your body and your baby, and you really do have to do what is best for you. Don't let anyone make you feel bad for that.
If you do want to keep going with breast feeding or do combination feeding, then consider getting some nipple shields, I ended up buying some after getting mastitis, and they do help with the rawness. We're doing mostly breast feeding now, with the odd formula feed, when I'm too exhausted, and my DS switches happily between breast and bottle, so there's nothing to say you have to do one or the other. Being able to hand him over to someone else for the odd feed is a godsend, and my nipples get a rest which helps a lot. I had massive guilt about it originally, and cried for most of a morning over it, but it's the right thing for us, I also got to a point where I couldn't carry on and had a bit of a breakdown over feeding, and so combination feeding was the compromise.
The other thing I will say is that my baby feed constantly on nights 3 and 4, literally for about 7 hours at a time, with no more than about 20 minutes sleep between feeds. It was exhausting and I was a wreck. But once my milk came in he did slow down, and the feeds have spaced out a good bit more now. Google cluster feeding, it often happens around this time, it's baby's way of making sure your milk comes in and that you're making enough. No one warned me about it, and I was very ready to give up by the end of the second night. Thankfully my midwife was very reassuring about it slowing down, and she was right, it doesn't last forever.
You have to do what you need to in order to give your baby the food she needs, but also, crucially, a mummy who's fit and able to care for her. That means you being mentally and physically ok. If you're dreading feeding times, and working yourself up over it, then you absolutely need to make changes. A happy mum is vital for your baby. So don't be too hard on yourself, it's tough, but you're doing great, I promise. xx