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My name is ***** ***** I have been a Vet tech for 30+ years with special interest in reptiles and reptile rescue. The Antibiotic will not injure the eye. It more than likely just irritated him a bit. You can use a Sterile Saline Eye Drop without preservatives in the eye to soothe it. The bubbles you see from the nose or mouth are a result of the Respiratory issue. you may even see crooked swimming from Raphael, which comes with this of problem.
An oral antibiotic is not always the easiest to give in turtles, so the problem you had is to be expected. Please do not worry as long as you are able to medicate Raphael, he should recover from the Respiratory.
Make sure your UVB light is new than 6 months old as that helps boost the immune system. Please let me know if you have further questions. When I have addressed your concens please rate my Service 5 Stars.