Asthma is a type of bronchitis (bronchitis is just a fancy way of saying inflammation in the bronchial tubes), so yes, shortness of breath can occur with bronchitis.
You might want to avoid eating a lot of dairy products until you are over this infection - dairy proteins promote the production of mucus and you already are dealing with enough of that without adding to it.
I hope you feel better soon. Take care,
Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication Allergies & Intolerances, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD (Lupus?), Osteoporosis, Anemia, T- & B-Cell Lymphopenia, malabsorption/malnutrition, Lyme Disease (Igenex Lab IgM WesternBlot positive/CDC negative), etc.
Meds: Pulmicort, Injectable Vitamin B12, Herbs, Nutritional Supplements, Homeopathy.