Could I still have bronchitis or pneumonia without a fever?

I have been coughing very hard all morning and I feel light headed and tired. There is phlegm when I cough and I threw up once so I think I may have coughed til the point where my gag reflex was triggered. Sometimes the coughing fits are painful. I had a cold not long ago but I'm not experiencing any nasal congestion or a runny nose so I don't think it could be post nasal drainage. I'm short of breath, but I have no fever... does this rule out a bronchitis/pneumonia diagnosis?