What antibiotics are you giving?
You mention it popped? Does she have a discharge?
That did look like a soft shell egg and since it wasn't expelled, it may still be in the oviduct or it could have traveled back up the oviduct and is now in the abdomen (
Internal Laying).
I do not see how this could be your fault though, there's no sense in even going down that road. Internal Laying, Egg Yolk Peritonitis, cancer, tumors, etc. sadly, these are all common in laying hens. While it's not as common in new layers, it's not unheard of.
Laying double yolkers and extra large eggs....you had nothing to do with that either. Double yolk eggs are from 2 yolks being released and incorporated into the egg. This can also be common in new layers.