Can bronchitis go away on its own ? without medication?

Viral Bronchitis: Yes. Of course. Many winter respiratory illnesses are caused by viruses and these often clear up on their own.

If it is viral: Then it can go away on its own.

Yes : More than 90% of bronchitis episodes are viral illnesses from which one should recover from with time and antibiotics are not necessary. If the bronchitis lasts more than 3 weeks then a chest x-ray is warranted to make sure there is no pneumonia, in that case antibiotics could be tried out. Also if you have other medical problems that predispose you to bacterial lung infections..Talk to your doc !