As a busy international business traveler, exposed to all sorts of virus and bacteria, I've tried and tested a lot of remedies. I've found the single most effective mucalytic is fluimucil (acetylcysteine). It's over the counter in most countries. One tab in a glass of water like an alka seltzer. Symptomatic relief in minutes. No drowsiness either.

Breaks down phlegm -> Reduces throat irritation -> Reduces coughing -> Reduces spreading.

Once the phlegm is under control, it's much easier to figure the rest out.