I was diagnosed with acute bronchitis by my gp. I'm on my second course of antibiotics but the pain in my back is. Not easing?

Cough. Cough can caused chest wall pain. If having fever, worsening cough, shortness of breath etc then need to go back for reevaluation and further testing.
NSAIDs? People with acute bronchitis can develop pain from either coughing too much or even from inflammation of the the lining of the lungs (pleuritis) that can be associated with lower respiratory tract inflammation/infections. Otc NSAID are a good starting point for both. If they dont help, the primary md should be notified.