Hi Lisa,
I'm so sorry you are having so much trouble with this poor little guy You're a trooper!

I believe the vet may treat him for parasites without a fecal ?
I can understand why the vet suggested to keep going , perhaps thinking a few more days may make that difference?
I'm sorry I do not know if vomiting is a symptom of the Baytril? I suppose it's possible?
Baytril is a strong antibiotic. It's simple - either it works or it doesn't. Perhaps that is the vet is trying to determine?
So keeping in touch with your vet is a great idea as I'm sure the vet will know what to do next.
Especially when kept up to date regarding how your frog is currently doing.
Can you email your vet? If so, this is a great way to give precise /dated/ details.
Plus the vet can ponder on the information you provide.

I am, however, certain vomiting is a symptom of more than one type of a parasitic infestation.
Other symptoms could include less activity, no appetite , and even blood in the poop
One type of parasite called nematodes initially causes diarrhea. If left untreated, the infestation can spread to the lungs and cause respiratory distress.

His antibiotic could be changed also?
There is another ( Metronidizole ) that will simulate his appetite.

I have ( under a vets recommendation) used metro and panacur ( parasitic treatment) at the same time to treat a black eyed tree frog. Initially it was done WITHOUT a fecal because the frog was so sick. I had to force feed this frog and use reptiboost for 7 weeks. I can sympathize with you; this is hard work.

Keep us posted
Lynn