Help with lash eggs

[Salmon1000]

Hey so..i am not a usual chicken owner or anything but, a couple of weeks ago a random chicken appeared infront of my house, so i took it in, it seems to be a laying hen and seems to be doing alright apart from soiled back feathers, while the oviduct of the chicken seems clean.
She eats very well, drinks water, runs when she wants, chatters a lot, even tries to attack the cats when annoyed and has a healthy colour and everythng, however, she layed a pink tiny slimy thing, we inmediately got her on enrofloxacin and apple cider vinegar in her water.
The following day she layed a shelless egg (which we attribute her being thin and dirty when we first found her) and many more tiny "lash eggs" and seems even more alert, i don´t know if that´s good or what, we already have someone that wants her as a pet but we don´t want to give this hen away until she is healthy again, plus i care about it already. What indicators can i look for that she is getting better?, i know that laying one lash egg is a bad thing but i don´t know if laying a lot of them the following day of being given an antibiotic means that she is getting rid of the infection in her body or a bad thing.

 

[turkey girl 0964]

Here is a good article that might help you:https://www.backyardchickens.com/articles/commom-egg-quality-problems.65923/

 

[Salmon1000]

Here is a good article that might help you:https://www.backyardchickens.com/articles/commom-egg-quality-problems.65923/

Thank you, i´m really at a loss here, i haven´t had chickens before, i cleaned and cut her back feathers to keep her clean but think she is also a bit swollen, i think, because i never had a chicken so i really have no idea