Why Does My Lung Hurt When I Breath In Or Out?

It could be Pleurisy. Get checked by a doctor if you have any symptoms for pleurisy.

Pleurisy (pleuritis) is a type of lung inflammation that causes sharp chest pains when breathing. The pleura is a membrane made up of layers of tissues that line the inner chest cavity and a layer of tissues around the lungs. When this membrane becomes inflamed it leads to pleuritis.

Pleuritis leads to chest pains that worsen when breathing; when we breathe the pleura rubs together. When the pleura is not inflamed the rubbing together does not cause pain because no friction is being generated, but once inflamed friction occurs, it leads to pain.

Although pleurisy was once a serious and even life-threatening condition, it is not nearly as common any longer; medical advancements have improved treatment and become better at preventing bacterial infections, which can lead to inflammation.

I have a pain in my right side  by my lung it hurst more when I breath in I had it for more than a week now.

Is there a cough, wheeze, or fever? Because pneumonia itself may make a patient cough, feel short of breath, fevrish and weak, but when the covering surface of the lung becomes inflamed, pain may result as well. Both lungs are covered by a double-layered envelope of membrane that has a rich supply of nerve endings. These membranes are called the pleura, and when inflamed, infected or irritated pleurisy results.

Are you smoker and/or are you on the contraceptive pill?
If so, and you experience chest pain, a pulmonary embolus should be considered urgently. This is a blood clot in one of the major blood vessels within the lungs. Where there is a complete obstruction of the blood vessel, tissue death in the area of right lung supplied by the artery will occur, causing sudden chest pain.

I am not a doctor, but better to go and have a checkup.

Its could be a  chest cold possible (bronchitis)! Or if you smoke then can cause pains in your lung during both inspiration and expiration.