Burning in back when I cough?

Back pain. When you cough you increase pressure in your chest and abdomen. You also forcefully flex the spine. Back pain when coughing can be from irritation to paraspinal muscles when coughing, or it could be from a disc being pushed on during the force of the cough. A few episodes of this is probably not a concern , but if this persists or worsens i would get it checked.