Can Z Pack Be Used For Cough With Mucus?

In March, came down with some type of cold, lost voice almost, got a bit better. Then I got sick again, small cough, fever of around 100-101.5. Self medicated with amoxil 500, and seemed to go away. 2 1/2 weeks later, chills, low fever 101 at highest but normally around 100.2, and cough came back. Strange fever - would break during night and I'd wake up w/sweat like my clothes came out of washer, then around 2 or 3 p.m., fever come back with slight chills, would go to about 100 or so... then it would repeat. This went on and off for about 10 days, and the cough started getting worse. Over the course of May, the cough has continued. No fever/chills now at all. The cough has been so severe a couple of times that I did almost throw up... couldn't stop coughing. Lying down is worse. I don't hear any indication of crackling in chest with scope. Bringing up light to dark yellow mucus, mostly thin, but couple mornings it was a thick blob. No ins., will z pack fight it?