Well you sound like a lot of patients I see on a daily basis who expect an antibiotic in this context, but I try to talk them out of it. Even with fever, sputum (doesn't matter what color), and sinus congestion the statistics suggest you are recovering from a viral infection. If you are short of breath, see a doctor. If not, stay hydrated, use some Tylenol, keep moving (don't lie around all day), and if you notice incremental improvement over the next week, you are following a typical trajectory for a viral upper respiratory infection.

I'll often give a Rx for an antibiotic to a pt like this who can't leave without it; but we make a deal that they won't fill it for 3 days unless they worsen... almost without exception they gradually improve over 3 days and never fill the prescription.

Cough can last up to 6 weeks in a normal non-asthmatic non-COPD individual following a viral URI. Frustrating, but not pathologic.