I would suggest both drops in the nostrils and also give it to your cat internally. Add about an ounce at a time to his drinking water for now. When he gets well, then you can reduce the amount. And yes, this will clear it up.
DQ
In no way are you going to poison your cat with colloidal or ionic silver and it is very unlikely that any blueness in the gums could be caused by only a few drops of silver this soon. However, you should make sure that you are not contaminating the silver with salt (such as might be found in saline solution), since it will contaminate the silver and may result in the formation of silver nitrate, which COULD causing staining over time.
Besides using nose drops you should also put a few teaspoons or tablespoons of silver in your cat's drinking water. Your cat will love it and it will help with the infection as well as the overall health of the kitty.
Again, your cat is NOT going to be poisoned and the key to best results is to use a lot of high quality silver. I am not a fan of Silver Shield. I consider it an inferior product when compared to Utopia Silver or Mesosilver and personally would rather use the quite adequate silver you get from a Silver Pupply home generator than the Silver Shield product.
DQ
(Ruh Roh - I see that the first time I attempted to post this answer, once again I managed to post as Luella May! Arggggh! I bet the multiple ID conspiracy nuts will have fun with this. We are currently using the same computer and logging on and off has been a comedy of errors a few times - lol)
Unfortunately, most health food stores carry inferior silver such as Silver Shield or Sovereign Silver because it is marketed to them and they get a better deal. You get Utopia Silver's colloidal silver by scrolling down this page and clicking on their link in the CureZone sponsors box.
You should not use silver and saline solution at the same time. Salt plus silver equals silver chloride and it can turn you blue (look at the blue man, Papa Smurf Karason - that is what he did) though it normally takes a very large amount and a very long time. You should be OK if you use them several hours apart.
DQ
If it were me and the antibiotic were not working, I would nebulize with colloidal silver or ionic silver and I would not use saline solution at all. I would also absolutley add a few spoons ful of silver to the drinking water.
DQ
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