Can't stop this phlegmy cough!

Ok, so I got attacked by something. It pretty much resembled the flu. All the typical symptoms and I simply did all the typical remedies. Soup, garlic, tea with lemon juice and honey, hot steamy showers, and 14 hour sleep sessions. The highest my fever went was 100.7F, not THAT bad, I've had worse. Three days later and the fever is gone, the muscle pains are gone, the weakness is gone.

So why isn't this phlegmy cough and runny nose gone?! These two disgusting things are still lingering around, now almost 48 hours later. The cough is always deep and phlegmy, the mucus of the nose is clear. It's leaving a bad taste in my mouth, and a bad smell in my nose.

I'm weary about using antibiotics unless absolutely necessary. Is this an absolutely necessary state or can I just wait this out and it'll eventually go away...