My infection came from bad contact lenses and solutions; but yes, I think taxing your liver is not a good thing. The floaters are, I believe, the degeneration of cells, which then get stuck in the eye fluid; hence the noxious chemicals from the Antibiotics have immediately caused a degeneration of the cells. My father had one that bothered him a great deal and I don't think it was resolved (but age there was a factor).
As far as I can see one is like a little spotty knot and the other is like a snake with a head and tail.
You might try cold compresses and/or a clay pack over your eyes, but I don't know too much about this. You might want to consult Raymond Dextreit's book on clay "Our Earth Our Cure".
And I would continue with the herbal eye drops, they may help guard your eyes against another infection if there is weakness in that area.