hey - i'm kinda learning about this area...yeh i know odd! I'm not a medic or anything though so cant really advise on that side of things.

Ear infections are unfortunately rather common and painful - i've had a few myself. I've never heard of the homepathic remedies others have talked about but to be honest it won't clear the infection if thats what it is intended to do, as infections are in the middle ear behind the ear drum and you'll only be putting things in the ear canal. Thats ok to get rid of wax etc but not needed for infections.
You said when you were younger and had your tonsils out that your ears popped - do you mean you have a hole in either of your ears because if this is the case you are more prone to infections and should most certainly not put anything in your ears at all, not even let water in if you having a shower etc.
Anti-biotics are the best things for infections - it must be bad if its still not clearing after 3 doses. I feel for you! If things do not clear up then there is the option of grommets but that is only if the infection is recurrent and significant (plus it isn't effective if you have a perferated ear drum). And is an option a long way down the line.
Lymp nodes swell because they contain bacteria to fight infections - it's a good sign but sometimes they can become over burdened. Your dr is right they can become swollen due to allergies (i have no idea why haha).
As for the garlic oil - i've heard it does have an antiseptic quality and i've heard ppl have it when they have tooth ache but not for ears but its a good idea. But again if you have been told at all you have a hole in your ear do not put anything in!

Anyway sorry for the essay. I feel for you. I've seen many people with ear infections and it ain't pleasant!