When DD was young, she always fell asleep too, nothing worked, she just slept, so I fed her every single hour of the day. No exaggerate. She also did the fussing at boob, probably coz there wasn't enough and she was impatient to wait for them to refill. I just endured, cuddled her when she fussed, tried to distract her till they refilled, and just kept it all up and then suddenly (I think it was 8 weeks) everytihng fell into place and it was a breeze.
It all sounds normal what you're going through, just know it all falls into place sooner or later, and just keep breastfeeding all the time, and call ABA everytime you freak out!
Best of luck!!