What Causes Nose Bleed After Treated Chest Cough?

I ve had a phlegmy cough now for 2 months (probably a chest infection). I ve been taking cough mixture for chesty coughs but it doesn t seem to cure it. Now for the past week I have been having slight nosebleeding, mostly in the morning when I get up. Does this mean it is now clearing the infection or should I go to the doctor.