I totally know where you are coming from! You need to block feed - nurse only on one side a feeding and for a certain time period any time she is hungry, feed on that side. So for a 4 hour blockfeed, if you nurse on the left side at 12 and she is hungry at 2 and 3, nurse on the left side. Then if she is hungry at 4, nurse on the right side.
What I would do that helped to take care of the engorgement (my DD couldn't even latch on, it was like latching onto a brick wall!), I'd stimulate a letdown (which is pretty easy in those early days) or you might be able to just lean over the sink and have milk come out. Then I would lean over a sink and hand express (basically gently squeeze the whole breast - my nips were tender!) until I was comfortable on both sides.
Between the blockfeeding and the expressing, this helped get it down to manageable portions. If the 4 hour blocks don't work, you can go up to 5 and then 6 hour blocks. The first 3 weeks were a blur of milky shirts for me though, so it might take a while.