I have had bronchitis many, many times. I agree that your symptoms sound like bronchitis; the deep cough & tight chest are classic symptoms.
If I were in your situation, I would find an urgent-care clinic, like Jinga & strawberry suggested. If there's not one around, I would go to the ER. Bronchitis can lead to pneumonia, and shortness of breath is always something you should see a doctor about.
Feel better soon!