I'm not an expert, I just had 8 eggs hatch. They were shipped, and some were in the wrong place in the egg...air cell on the side, etc. I helped most of them hatch.
This is what I did. Not what you should do, but this is what I did, maybe it will help a bit.
I enlarged the pip hole (you're past that!) and peered inside. If I could see veins and they were obviously swollen with blood, I took a paint brush and painted the membrane with coconut oil to lubricate it and keep it from drying out. (Tiny, unused paint brush). Then, knowing the membrane was broken so the chick could breathe, I put it back into the incubator and waited. These were all on day 21 and starting to externally pip. After some hours I looked again. If the veins were still obviously containing blood, I put it back.
But finally, I could see the veins had shriveled up and been absorbed. At that point I carefully peeled off tiny pieces of shell to enlarge the hole...all the while stopping if I saw any blood-filled veins. (When the dried up they looked thready and pale orange, before that they were dark blood color and thicker). So you need to see the veins to check whether your chick is ready to come out or not. If you break veins too soon the chick will bleed out.
With mine, after I waited...lubricated...waited...and so on, the chick came the rest of the way out on its own. If your chick is ready to hatch, which it should have been on day 21, it shouldn't die with a piece of shell gone.
I actually ended up removing shell, lubricating, peeling back membrane that had no veins, and enlarging the hole to give mis-positioned chicks a hand. They all survived, except one that is now 2 days late...I thought it was dead but it began pipping tonight and I've been helping it. Now, some folks say "don't help a chick hatch'' and others say it's ok. Mind you, this is my only first time, so I'm a rank amateur.
But maybe this will help you a little bit. GOOD LUCK and do not beat yourself up!