What Causes Persistent Cough Along With Irritation In Nose?

I have been coughing badly since august 2014 and now its january 2015. I've been prescribed tons of antibiotics which helped it for a couple of days, and then the cough got even worse. I also have an irritation in my nose so I'm taking Flonase nasal spray. Since my mom and aunt have asthma which caused HORRIBLE coughing during certain seasons, I'm taking asthma medicine called Singulair which isn't helping me at all. I have no idea what to do. Also, in August I got a respiratory infection and in late December, I got a sinus infection. This was in addition to coughing. Also the coughing does not help me sleep at all.