I Had A Chest Infection In January And Ever Since

I had a chest infection in January and ever since I finished the course of antibiotics I have still been coughing daily n constantly clearing my throat, I play sport and at full excersize breathing is hard, my doctor says it's my sinuses but I havnt had any nasal congestion or sneezing bt wen i cough sometimes I feel lik I'm winded and can't draw my breath, any explanation for this or anything i can do!?