This sort of thing drives me potty; the majority of ear infections don't respond to antibiotics. Quite often they are fungal or viral, with a bacterial infection as a secondary invasion, as it were. Also, ear infections often start as an irritation in the ear canal, which then creates an opportunity for a secondary infection - blasting these with antibiotics can be counter productive. If you have a rash on your arm, you would use a topical treatment for example, not oral medication
Ask your GP about a topical application, a pump action spray is usually best, rather than drops. Ask if Otomise would be suitable - its got antiviral, antifungal and antibacterial properties in it, and can be safely used for 7-10 days (but I don't know if its okay in children, don't see why not though) You have to use it for a couple of days after the pain / wet / itching stops, but its very very effective even if it does smell like vinegar! There's no reason to keep taking oral antibiotics if a topical spray will do the job and do it better
Good luck, sorry if I sound stroppy but it drives me mad!