What Causes Nose Bleed After A Fit Of Coughing?

Hello, I recently had cold symptoms which cleared up, then I had the flu from Christmas Eve onwards, I am just starting to feel better but I have been left with a chesty cough. I have asthsma so its a quite persistent, nasty cough. I had a slight stomach upset yesterday but more this morning when I blew my nose I had a nose bleed after coughing. I never suffer from nosebleeds. Do you know what could be causing this? Thank you