A burning pain when you breath deep can have several different causes. The best type of physician for you to see about this type of discomfort is a primary care physician
such as a family doctor
or internal medicine doctor
The most common reason that people get a burning pain during a deep breath is because the lining of the lung is rubbing up against the lining of the chest wall. We call this pleuritic chest pain. Some times the pain is simply caused by inflammation of this lining and simple anti-inflammatory drugs will help out. Other times this pain is because of an infection such as pneumonia. Finally, a pulmonary embolism (clot in the lung) can cause this type of pain. This is usually associated with sudden shortness of breath. Occasionally, problems in your abdomen can cause pain when you breath deep.
I suggest that you schedule an appointment with your primary care physician. He or she can take a more detailed history of your breathing symptoms and perform a thorough chest and abdominal exam. Depending on the severity of your symptoms and the findings on your physical exam, you doctor may decide to get a chest x-ray. Hopefully, you will get to the bottom of it.