I think the doctor is right and I'm trying to find a good diagram to show you. When you drop something into the ear, all it's going to hit is the ear drum which is not the problem causing the infection at all.
My daughter has had an ear infection on and off since early December and I have one now (yay, allergies, awesome) so I've seen a LOT of these diagrams (seriously, they can stop showing them to me now, even my five year old can name all the parts of the ear). The infection is behind the ear drum and it's being caused by a blocked tube on the other side of THAT so whatever you're dropping in isn't getting anywhere near the actual issue.
It just doesn't make sense that a substance dropped on the ear drum would really do much.
There are a few things I've been doing to make us more comfortable (steam! sometimes that will cause the tube on the other side to open up and drain and if it doesn't, it seems to at least take some of the pressure off the ear drum) because abx and decongestants don't work as fast as we'd like, but other than that I just can't see how dropping something into the ear would work. If that worked, the doc would prescribe ear drops.
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