If she has an infection and they put her on Baytril, make sure and give her something after you give her the oral Baytril. The Baytril tastes horrible so it tends to make chins stop eating, which is the last thing you need with her weighing so little. So if you do get Baytril, you can chase it down with a piece of raisin. Don't be overloading her on raisins or anything as the sugar isn't good for them, but one after the medicine will be fine to get rid of the horrible taste. Also, Baytril kills off their bacteria in their digestive system that digests their food. So you're going to need to get some probiotic to give to her about 4 hours after giving the Baytril. This will help get the bacteria back up. You can get probiotics at health food stores, you want either a capsule that you break open onto their food or a tablet. Just make sure that the active bacteria count in them is in the billions.
Also, I would get some Critical Care from your vet if they have it, in case she does stop eating completely. Most chins it seems prefer the Apple Banana flavor. If your vet doesn't carry it, you can order it online. It's a food replacement and also has probiotics in it.
Perhaps they will prescribe a different antibiotic, as there are others that aren't as horrible on the chin's digestive system as Baytril, but that's up to your vet.