Some people use pinless peepers on the bully, so she cannot focus on an object to peck. I haven’t used them, but many say they work. Here are places that sell them, as well as Amazon if you look around, and some use a separate plier to apply them...
Sorry that they are still picking on her. Maybe try the wire dog crate with food and water, and allow the crate to be with the others at all times. Pinless peepers can help if it is just one or two hens picking on her. I hope it gets easier.
I would clean off the scab with saline and put some Neosporin ointment on it twice a day to keep it from drying out. Yes, laying a shell-less egg can make them feel lousy, and sometimes there can be another egg on the way.
I would give her a human calcium citrate tablet for the next several days to a week, in case she is low in calcium or having reproductive disorder. Stress, a defective shell gland, reproductive infection, being a new layer, and low calcium levels are some causes of shell-less eggs.
Is that (bullying) how her comb was first injured? I don’t like to separate chickens outside of the coop unless necessary, but 10 days could bring some pecking. I would put her out and stay there for awhile. When I bring back broody hens from their pen after 5-6 days, they may get chased and...