Coughing over a month. Diagnosed with bronchitis. Got better. Cough returned. Barking with metallic taste. 37 weeks pregnant. What should I do?

See your doc. Though you said you got better from your bronchitis, i think you may have had a relapse and might benefit from another course of a different antibiotic. There are a number of safe antibiotics you could be treated with so see you doctor and hopefully you will be feeling better before you go into labor.
Check with doctors. You do need to get better. Your doctors are best to work together to come up with the safest medications.