Chickens act like they are fine until they drop dead. It's a survival mechanism. I'm sure there's nothing you could have done to save her.
You can send the body of the chicken to your State Vet for a necropsy in some states, and they will tell you what the bird died of.
Unless you know what specific disease you are treating, using antibiotics is a bad idea. If your chickens have a fungal infection, it will make it much worse and may kill the chickens. If they have a virus, it will do nothing. If they have a bacteria, it might kill the bacteria or it might not, because different antibiotics are formulated to kill different bugs.
If you do not treat the animals with the antibiotics for ten days you risk killing the weak bacteria and giving the stronger ones the chance to reproduce, producing a super strain of bacteria that cannot be killed with antibiotics. That's why Terramycin no longer works on chickens.
One way to tell if a hen is eggbound is to watch closely and see if she is laying eggs. If you know a chicken is not laying eggs, you can feel her abdomen for any swelling, heat, lumps, and so on by running your hand from just behind her breastbone to her vent.
Sorry about your chicken.