Can depression and anxiety cause chonic shorrness of breath?

Yes: Anxiety can cause a perception of being short of breath.

Short of breath: If symptom occurs during the episode, yes. If occurs consistently or have history of breathing problems or is progressively getting worse, then u need medical workup.

All or episodic?: If you mean your shortness of breath during episodes, the answer is yes. If you mean that all of the time, while sleeping, relaxing etc, no. Depression and anxiety can cause these symptoms, but are not the organic cause of breathing problems, which if exist should be explored by a pulmonologist.