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patient states they can't breathe easily--this is dyspnea
patient states they have chest pain with breathing--this is chest pain
These symptoms match with the defining characteristics of the nursing diagnosis Ineffective Breathing Pattern. That is the patient's nursing problem.
The next steps are to develop nursing interventions for the dyspnea and pain the patient experiences with breathing and the goals (I think you call them objectives in the Philippines) of doing these interventions.
Going another direction: You may want to address the chest pain as the primary issue. Difficulty breathing can be caused by cardiac problems. This certainly does not mean that breathing problems don't cause chest pain (i.e. pleuritic chest pain), but at least you have the more life-threatening issue covered first, just in case.
Second, I would make sure to rule out pneumothorax if this is a new-onset problem.