Diarrhea, headache, chills, upset stomach, feel feverish but no fever. On antibiotics and have bronchitis. Is this normal?

No. Bronchitis is usually due to a viral infection which will not respond to antibacterial antibiotics. You could have chronic bronchitis from your smoking. You may have antibiotic associated diarrhea or clostridium difficile colitis. Get checked out again by your md and stop smoking.
Maybe not. Patients on antibiotic therapy can develop a secondary intestinal infection called c. Diff colitis. This presents as diarrhea, abdominal pain and fevers. I would consult your prescribing physician and ask him/her about it.