Did the vet culture the RI? Did he explain his choice of antibiotic?
Did your vet advise fasting the snake while administering the amikacin?
Amikacin is potentially toxic on the renal system so the animal should be well hydrated and fasted to keep the kidneys flushed. It is important that since you are dosing your snake for a month that this information be given to you. It is also important that such information come from the vet prescribing the medication.
I've never had any health issues related to RIs or scale rot due to low humidity. To the contrary, you run a much greater risk for both if you raise the humidity and do not provide enough ventilation. Maybe the vet can explain the mechanism in which humidity in the 40% range leads to URIs and scale rot. I'd be very interested to hear it.