There really is no such thing as a "stronger" antibiotic. Your snake's respiratory infections is caused by a type of bacteria, and that bacteria may be gram-positive or gram-negative or something else. Each antibiotic is made specifically for a type of bacteria. Baytril is relatively broad spectrum, but not fool-proof, meaning there are still types of bacteria that are resistant to it. Even so, Baytril is actually becoming an "older" way of thinking when treating reptiles for infection. The vets at my hospital (I am a vet-tech) do not jump straight to Baytril anymore for snakes, mostly due to side-effects such as injection site necrosis resistance and resistance due to over-use in the reptile world. Fortaz/Ceftazidime tends to be the more "modern" drug of choice.
Amikacin is something you have to cautiously use in reptiles because your animals must be VERY hydrated in order to withstand the drugs... A non-eating animal is usually not a good candidate for Amikacin.
What someone mentioned earlier is the way to go: doing a culture or lung wash, sending the sample out to a lab, and seeing what kind of bacteria it yield, and what meds it is sensitive to (rather than resistant to) is the way to go. It's not necessarily a matter of finding a "stronger" drug, but the "right" drug... If that makes sense!
It's common practice to medicate broad spectrum first rather than doing a culture in the first place, so don't be ma at your vet. We always recommend it to clients, but most financially conscious people turn down the recommended culture, and go for conservative treatment: they would rather try broad-spectrum meds first, with the understanding a culture will be needed if the patient doesn't improve. This is where you are at now! 
Hope this helps!
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Cheers!
• Chelsea Lynn Gardiner
(and Frank M. Wood)