Do i have bronchitis? had a cold which worked itself into my airways. coughs are productive. cold&laying irritates. will it resolve itself?

You're ill: If you have had a productive cough for 7-10 days with other illness symptoms, it sounds like a bronchitis which may warrant antibiotics. There is a possibility that you can heal a bronchitis with your own immune system -- most people simply decide that they are sick of being sick and elect to speed along the healing process along with medical/supportive therapy. Continue with fluids, rest & soup.

Treatment...: Bronchitis is an infection in the airways usually due to either viral or bacterial infection. If you have symptoms like fever, discolored sputum ( including bloody), etc. And it is not improving, it is more likely to be due to bacteria which should be treated with antibiotics. You may also need bronchodilator and steroid inhalers. See your doctor for diagnosis and treatment.

Yes: 95+% of cases of bronchitis are viral and that is what it sounds like you have. If you are a smoker, stop. If not and this does not go away in the next several days or you develop fever, go and see a doctor. Remember that if you damage airway tissues you cough up the material damaged and cannot be otherwise cleared by the usual mechanisms. Hope you feel better soon.