so engorged my baby won't latch

Shannon
Hi ladies! You will probably be seeing lots of me here as I'm so excited to be breastfeeding. I'd like to share my story so far followed by a question (please scroll to bottom for question if you want to skip story!!) 
My baby girl was born a week early due to IUGR on 9/23. We have had the WORST breast feeding journey so far. She latched right after birth but I had no idea what was happening and it was so shallow that she murdered my nipples (we switched sides). After that, we got what looks like the perfect latch but isn't because it is painful and my nipples come out bleeding!! None of the LCs at the hospital believe me because it "looks so good". I found a LC outside of the hospital to help. We finally started figuring out bf and now my milk is in and my boobs are so engorged that she CAN NOT latch. I've heard not to pump as it boosts supply. The internet says to put my breast in hot water and hand express until she can latch, but that's hard with a screaming baby! 
So, how long does this engorgment thing last? When will I see improvement or is it overnight that it goes away? What are some realistic ways to help my baby latch without being so frustrated?