Suggest Treatment For Severe Dry Cough While Having Sinus Infection

I have had severe sinus congestion. developed a barking cough, ended up having in initial diagnosis of sinus infection and inner ear infection. received a round of Keflex...cough never went away. last day of antibiotics I wa prescribed the steroid pil, starts with a m. (long word) and tapered off of that. still have cough after another round of Keflex a week after the previous 10 days of Keflex. Now sinus infection I feel has not completely gone away. thick mucus still, congestion in ears and sinus cavity are still thick, yet no signs of purulent. feels like there s an obstruction practically hanging down the back of my throat from the upper sinus/naval cavity...still have the cough. its been a month and a half of this ongoing... was taking 400mg of expectorant 3-4 xs daily for a month straight. changed different brands, followed advice. still have a problem. not as bad as I originally hd it but still...idk what to do. no insurance so makes it even more difficult.