I would not put straight Lugol's
into the puppy's ears, for starters. I know Molly tried that and reported it to be very painful, and I have another friend who did the same thing and said it was "too much" -- and he is someone who does a lot of cleansing/detox pretty heavily.
A problem is that you don't know whether this is a parasitic problem (mites) or an infection (bacterial). I have had a cat with ear mites and you could see a sort of gooey brown sticky ickness in her ears...is there any kind of visual symptom you can provide? You don't want to treat one thing with a solution for another, so to speak. (This is where a vet would come in handy, for diagnostic purposes -- but I hear you on the $$$ front -- I never seem to get out of the vet's office without giving them hundreds of dollars...)
The necessity of treating an ear problem remains, though. The puppy is in discomfort, and the problem is a serious one in that the ear canals can drain throughout the head and mouth, so you can get a secondary infection (i.e. it may be mites, but the scratching, etc. could lead to infection).
One thing I have used with success (on me) is a few drops of Lugol's
in a base oil. I use this in my ears to clean and to distribute some Iodine
up there without the pain those others reported! I have used the Lugol's/coconut oil on scrapes my children have gotten. You might try that in the puppy's ears. Extra-virgin coconut oil is a potent anti-parasitic and anti-viral agent. (I put some in a small jar, add a few drops of Lugol's, and shake it to disperse the iodine.)
Another thing to consider is the Humaworm for pets program. You should visit Ask Humaworm and describe your dog's symptoms to RG, who runs that forum. I used the formula with our new puppy and it was really helpful. (You add the powder to their food for several days.) We have a ton left over as he only used a small amount of the adult-dog dose, which I am happy to share.
Hope your pup gets better quick -- I know how horrible it is to see them feeling bad and not know what to do about it.