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.
In most people, sharp chest pains with deep breaths, especially with hard exercise or while breathing cold air is a perfectly normal finding which simply represents the sensitivities of the lining of the tubes inside the lungs to the fast flow of air or the cold.