Cough for 3 weeks after having a cold. Acute bronchitis?

[DennisQQ]

I had a cold from 02/17 - 02/26 and then I got another cold from 03/03 - 03/16. Symptoms of my cold were runny nose, cough and congestion. Every morning I would spit out green phlegm and afterwards it would be clear. So on 03/16 everything cleared out, no longer had any cold symptoms; although I was left with a cough, somewhat tight chest and short breath. There's no mucus, it's a dry cough and any mucus I spit out or blow out is clear. Is it acute bronchitis or should I visit the doctor?

[DennisQQ]

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