How many days has she been doing that for? Maybe it's a growth spurt? She's right around 6 weeks, right? I know they say it's about 2 or 3 days, but a growth spurt makes things go funky for more like 5 days to a week if you ask me.... it's just 2 or 3 days that are really horrible.
If you don't have any other issues going on with nursing, try switching sides after 10 minutes or so and make sure she gets both sides at each feeding (I know, it feels like you're just going from one side to the other and then straight back again when they're frantically eating like that) It might help your body figure out it needs to increase your supply quicker.
In the meantime, try and get as much rest as you can, even if you can't sleep. Try using some of the coping techniques you practiced for labour, or try meditating. You don't have control over how much sleep you get, but you might have control over whether or not you're distressed by the lack of sleep.
We're in the same boat. Ds was born on the 6th, so close to the same age.... I just switch him from side to side all day long. And all night. Looking forward to this passing.