Is Bronchitis Usually Viral Or Bacterial?

Question : I had a head cold and thought it went away. About two days later I started coughing out yellow phlegm in the morning. Only in the morning and then during the day I was fine. I was also getting it from mu sinuses. I waited one week before going in to see someone. The two nights prior to going in I was running a pretty good fever. The night just prior to seeing a physician, my temperature was 102.5.
The next morning a DO said he wanted to give me a shot of Rocephin, after diagnosing me with bronchitis.
I politely declined. He prescribed me Augmentin. This was Thursday the 11th, so this had been going on for about 10 days. It was last Thursday and I went through the weekend without taking the Augmentin.
My questions. Could this be bacterial? I am not wanting to take this antibiotic, but I also do not want this advancing to pneumonia either. I do have occasional asthma occurrences, but only once in a while---when exposed to cats and dogs.
I asked the DO if there were a way to test the sputum to see if it was in fact bacterial or viral. He said they didn't do that and that the results would take too long to obtain.
I really do not want to take this antibiotic either, as I am reading that almost all cases of bronchitis are viral.
I also do not like coughing out all of this green gunk every morning, and still have low grade fevers at night.
This morning the green phlegm was tinged with a little blood.

ok
I am not concerned with the sinus infection. It will go away.

I am concerned about the bronchitis.

Can you please put me in touch with a pulmonologist.

Thank You