Feeling feverish but no fever. Allergies? Plus diarrhea, upset stomach, chills, and anxiety. Could this all be from my bronchitis?

Unlikely. These conditions are not related. See your doctor if the problem lasts more than a week or is getting worse.
Intestinal infection. It is not uncommon lung infection to have some constitutional symptoms but the symptoms you listed indicate that your problem lies in your intestine . You might have most likely viral intestinal infection . You mentioned also anxiety which also can be cause of diarrhea if not recognized and treated in appropriate manner. If symptoms persists, i would advise you to see your doc. Stay hydrated.