The transmission solenoids are located under the side cover of the transmission. The side cover comes off with the transmission still in the car, but it's quite a job, especially if you don't have a lift.
Injuries or conditions that affect the chest wall -- the rib cage and associated muscles -- are another common cause of pleuritic chest pain. Chest muscle strain due to strenuous exercise may cause pain experienced primarily with deep breathing. Vigorous activity can also lead to costochondritis, a condition involving inflammation of the connective tissues of the rib cage.
The type of pain that you are describing is probably not a pain coming from your heart. The reason I say this is that since the heart is on the left side of the chest, pain that originates from the heart usually stays on that side. Plus, chest pain that gets worse with taking a deep breath is usually not pain coming from the heart.