Should i still go to work if i have bronchitis?

Depends on severity: If you feel health enough to go to work and are able to do the usual tasks needed for your work, it is not likely to do harm. However, if you have bouts of cough, shortness of breath, fever, expectoration or bronchitis due to whooping cough, you should seek care before returning to work.

Perhaps...: If you don't have a fever or severe body aches, or shortness of breath, then you can likely go to work. Drink plenty of fluids and cough/sneeze into your elbow. Wash your hands often and avoid crowds. This usually has a viral origin so antibiotics are not needed or helpful. You will likely feel better in a few days. Rest as much as possible. Stay home and see your doctor if symptoms worsen.