This picture shows that your lungs are surrounded by 2 layers of linings. The inner lining goes inside the lung fissures while the outer lining is connected to the chest wall. There is a small layer of fluid between the two linings.
In your lungs, only the outer lung lining has pain-sensing nerves. To get pain from any problems inside your lungs, the outer lining must be irritated. When you have a blood clot inside a blood vessel supplying blood to part of the lungs, that portion does not get blood. That part starts to get damaged and inflamed due to the loss of blood supply. The loss of blood supply creates a wedge-shaped area that goes all the way to the inner lining of the affected lung. When the inner lining gets inflamed, it irritates the outer lining next to it, and you feel pain. It may take a while for the inflammation and irritation. The pain may worsen after some time has passed.
Pulmonary embolism chest pain:
If the section of the lung affected by the clot is next to your chest wall, you get pulmonary embolism chest pain. Pain from the irritation of the outer lining is very sharp. It can be felt over your ribs or your breasts. The pain gets worse whenever the lung linings are stretched. That happens when you cough or take a deep breath.
Pulmonary embolism back pain:
As you can see in the picture, the outer linings of the lungs cover a very large area, spanning across your chest, your back, and even a part of your neck. You can have pain from a pulmonary embolism in any of those parts. Back pain is very common with blood clots in the lungs. It is usually a sharp, stabbing back pain that gets worse with coughs and deep breaths.
Back pain from pulmonary embolisms can be felt in the middle or upper back. The pain could be on your left back or your right back. It may even be on both sides if you have blood clots in both lungs.