Think of DE as an exfoliant for the digestive tract. It will scrub the walls and flush out everything in your GI tract by physical action. It never leaves the GI tract and that is why it doesn't work on disseminated infections (systemic infections).
Drugs will permeate your system and kill pathogens by chemical action. Meds get in the bloodstream and are carried throughout the body.
It's better not to take both at the same time because the DE could remove some of the meds by flushing them out of your body. If you want to try both together, take DE first thing in the morning on empty stomach and wait til later in the day to take the meds.