Having said this, I'm not sure my son ever really opened his mouth wide enough by most people's standards. And, yes, the pain was excruciating. But, please know that our bodies are incredibly adaptable, so the pain will subside even if your daughter continues taking your nipple like a straw. It's just going to be a very rough few weeks. It's like running 10 miles without any preparation; your muscles are going to be incredibly sore, but if you keep doing it every day, eventually they'll be able to take the 10 miles without any problem.
Hang in there. It sounds like you're doing everything else correctly. Your nipples just have to get used to their new job. If you can put up with the pain for now, it will pay off. I went on to nurse my son for 4-1/2 years, and after those first few weeks, it was pain-free.