If the ear anatomy is normal, ear medication should stay in the ear. If she is having a reaction such as you are thinking the meds are going to her throat - she may have a ruptured ear drum letting the medication leak down further. I would definitely have concerns about this and withhold the treatment until your vet can look at the eardrum.
Please let me know if you have more questions,
Oh, I see. That explains it. I'm sure they prescribed something that is safe in this situation. Sometimes, especially in a small animal like a cat, the eardrum can heal. But only 1/3 left will be difficult.
Irritation from being intubated should only last 24 to 48 hours. It sounds like something else is going on with the throat. You should take her in first thing Monday morning for them to look at her. I don't think what you are describing is from the anesthesia or intubation.