Productive cough for nearly a week and a half?

I don't understand why I have a cough. It is disgusting and phlegmy. I am not sick, don't have a fever, but have had a cough for nearly a week and a half. It started off with me having a sore throat for a few days, and my glands under my jaw were swollen, but went away. Then, this cough-- I feel a bit congested in my sinuses, and I am prone to sinus infections; however, I don't have nasty colored snot or anything. How can I get rid of this cough? It is so annoying. I just want to feel normal.