Hi Chickenvirgin and welcome to the Forum.
If she has had diarrhoea ever since she arrived, that is concerning. You’re right that the stress of moving and of coping with bullying from the existing birds can often depress a bird’s immune system and cause them to go down with something they might have resisted on their home patch, but usually this happens a day or so down the line from their arrival. It’s always a good idea to quarantine new arrivals for two weeks before introducing them to your existing flock, as many chicken diseases are highly infectious whether bacterial or viral. If possible I would pen both of them separately during the day, and give them a temporary shelter or box to sleep in- it doesn’t have to have a perch. It’s not uncommon for newbies to have little appetite at first, but usually they can be tempted with nourishing treats until they settle in a bit. All may be well, as she is lively, and if they are given time to settle in quietly on their own, but it would really be good to keep them away from the others in a communal coop at night - for reasons we are all only too familiar with at the moment, since chickens can’t wear masks!
Where did she come from? Has she been vaccinated? Did you have the chance to check out the premises carefully? I would immediately contact the seller and attach photos and videos.Then if it gets worse you are more likely to get some help and redress. Do let us know how you get on with her.
