Is there a noticeable hole where this drainage came from that you are flushing? (Sorry - I may be reading your post wrong).
Without seeing the horse or the hoof it's hard to say what exactly you should or should not be doing. I would not, not treat the thrush if the horse has it. I'm assuming that when you clean the hoof you are seeing a white flaky area or you are smelling a foul odor to be thinking there is thrush. With as rainy as it has been and the bacteria in the mud, soaking in Epsom salt isn't going to hurt and would also help with any thrush. For the thrush you can spray a mixture of bleach and water onto the hoof or you can put the Koppertox on it. I like that thrush magic myself but I do always have the koppertox and it does work wonders. Don't squirt it down any holes.
"Be a best friend, tell the truth, and overuse I love you
Go to work, do your best, don't outsmart your common sense
Never let your prayin knees get lazy
And love like crazy"