Yes, nervousness and anxiety can lead to shortness of breath. When you are nervous or fearful, your fight or flight response is triggered when a part of your brain called the amygdala senses the fear and is activated. The activated amygdala then sends a signal to a part of the brainstem called the parabrachial nucleus (PBN), and when activated, it increases your rate of breathing.
Increasing your rate of breathing is adaptive for addressing a danger, as it oxygenates your body more to prepare it for fighting or running from the danger, and this can improve your chances of survival.
However, when you have extreme anxiety, like a panic attack, then the PBN is excessively activated, and this leads to shortness of breath, hyperventilation, or feeling like you are being smothered. When the PBN is inappropriately or excessively activated, it can also lead to worsening of asthma.