Cold has hung on for a couple of weeks, now includes burning chest pain. Constant barking cough. No fever. Should I wait it out or see a doctor?

Time to see Doc. A cold that is getting worse, or lasts longer than a week needs to be checked out. Sometimes when a person is suffering from a viral infection a secondary germ moves in too & that could be bacterial. An antibiotic can help then. Also stop whatever over the counter meds you are taking, since they are not helping, and sometimes make things worse. Stop using fragrances, avoid smoke, aerosols.too.