Having trouble breathing through your nose could have an effect on both, sleep apnea and the use and effectiveness of a continuous positive airway pressure (CPAP) device. What your psychiatrist suggests is correct.
The first thing to determine is the degree, and whether or not correction of your nasal obstruction is indicated. Much that you describe suggests obstructive sleep apnea (OSA). After the nasal obstruction problem is resolved, a trial of nasal CPAP would be appropriate. Also, if you ever experience sleep paralysis, the diagnosis of narcolepsy should be considered.
Also, one need not have a high apnea hypopnea index (AHI) or all the symptoms of OSA for the diagnosis to be present, with benefit from CPAP.