Is she a salmon faverolles? I have a couple of those and they are sweet. She really looks weak and worn out. Sometimes when they have a soft or shell-less egg, they may have trouble laying it, and become weak. Softies can be common in new layers. The white runny dropping is likely white urates, which can be from several things, possibly dehydration. I would glove up and feel inside her vent with one finger about an inch or two, for a stuck egg. Make sure she is drinking fluids, and offer plain water as well in case she doesn't like the flavored water. You can also give the NutriDrench in a dose of 2 ml daily into her beak instead of in her water. That can be less expensive, and more accurate. Offer some chopped egg, tuna, or liver in addition to her feed.