I learned of probiotics here. I think they are fabulous even for well parrots. I read the label, found it was many of the same cultures as found in yogurt. So for me I now prefer to feed live culture yogurt once in a while, fresh from my fingers or a spoon. Then I eat the rest

Hope your bird is better soon. Did you tell vet about the loose stools? It might be a symptom of his illness, or as you guess the meds. But the vet might switch the meds if it's to harsh on your bird.
Try feeding hit red chilli peppers, or any red , yellow or orange peppers. They have vitamin A that helps immune system. Conures seem to love peppers, and parrots species from Central and south America are considered nature's dispersers of peppers. Give the cage a good cleaning, so he doesn't reinfect himself.
I worry as mentioned to another poster about psittacosis, it's more common than most vets seem to think lately.... That's from my own excellent avain vet specialist of decades of experience. If he did have that, it would require a different antibiotic to treat. Baytril is a broad spectrum antibiotic, so it seems to a first choice. But let your vet know about the stool, it may change what they want to do. Hope your baby is better quickly!