Hello,
As per my clinical experience, the 
shortness of breath after 
severe sneezing indicate spasm of lower 
respiratory tract bronchioles most likely. Usually such episodes are in concern with:
   - Atmospheric allergen, pollen
   - Industrial dust
   - Secondary or primary smoke 
   - Congested places with inadequate fresh air
The resolution of issue depends upon the underlying cause of the condition and guide accordingly. Certain guidelines can definitely help him as:
- Avoidance of exposure to atmospheric dust, pollen, cold air
- Wear face mask wisely
- Avoid smoking if applicable
- Deep breathing exercises and YOGA
- Control of allergy conditions with anti 
histamine, 
steroids or else
- Balanced nutritious diet to combat the immunity
Hope I have answered your question. Let me know if I can assist you further.
Regards,
Dr. Bhagyesh V. Patel, General Surgeon