After the cold I still cough for month do I have bronchitis? If I do what do I do other than go dr. I cough with my troat irritation and lot a mucus

Bronchospasm... This cough is most likely the result of bronchospasm occurring after the initial infection has resolved. This type of cough may require bronchodilator and steroid inhalers. See your doctor so this can be evaluated and treated.
Mycoplasma? Mycoplasma pneumoniae infections occur in the average human about once a year. It is that dreaded cough which hangs on long enuf to make you think you have a cancer. Certainly there are many other illnesses which may be causing your symptoms. Do you smoke? Do you work around toxic fumes? Any other symptoms? More info would help.
Bronchitis. You are describing post-infectious bronchitis -- this is the residual cough that can last for 4-6 weeks after the acute illness -- you may benefit from an inhaler -- I would see your primary care doctor for an evaluation and discussion of treatment options.