Does she have a dummy? At four days old I had a 24 hour period where jack would feed for half an hour, stop for 15 minutes and them be back on the boob for half an hour for the whole of the 24 hours. I'd always said I didn't want my baby to have a dummy but after those 24 hours I gave in and gave him the one from the starter kit I'd been given. It made him sleep for two and a half hours, which was heaven!! He hadn't been eating all the time he was on me, he was comfort sucking, and so the dummy stopped that. If you're positive it's no longer a growth spurt (which can last different amounts of time for different babies, each one is different and suck a lot to 'put in their order' for more milk to be made) then maybe try her with a dummy, it will give you some relief.
As for the pumping hindering your supply, as long as you're not pumping a breast less than an hour before feeding, it shouldn't affect it as your breasts constantly produce milk, though you will naturally get more in a morning because of the extra hormones made overnight. If you have an electric pump you may need to try it on a different setting, make sure you have it pressed tight against you for good suction and it will help it you massage your breast and lean forward while you pump as this will encourage the milk to let down. Hope that helps hun and that you get some sleep soon xx