Musculoskeletal strain: This is the most likely diagnosis given the symptoms of rib pain that has moved to the back, worsened by twisting and bending. The mechanism of injury and the nature of the pain suggest a strain or sprain of the muscles or ligaments in the thoracic region.

Costochondritis: Inflammation of the cartilage that connects the ribs to the sternum, which can cause chest and back pain, especially with movement.
Intercostal muscle strain: Similar to musculoskeletal strain but specifically involves the muscles between the ribs.
Thoracic spine strain: Strain or sprain of the ligaments or muscles surrounding the thoracic spine, which can cause back pain that radiates to the rib area.

Pulmonary embolism: Although less likely given the lack of other symptoms such as shortness of breath or cough, pulmonary embolism can cause sudden onset chest pain that may radiate to the back and worsen with deep breathing or movement.
Aortic dissection: A serious condition where there is a tear in the aorta's inner layer, which can cause severe, tearing chest pain that radiates to the back.
Pneumothorax: Air in the space between the lungs and chest wall, which can cause sudden chest pain and shortness of breath, though the latter is not mentioned, it's a critical diagnosis not to miss.

Tietze's syndrome: A rare inflammatory condition affecting the cartilages and surrounding tissues of the ribs, similar to costochondritis but can involve the upper ribs and may mimic more serious conditions.
Sickle cell crisis: In patients with sickle cell disease, a crisis can cause severe pain episodes, including chest and back pain, though other symptoms such as fever or signs of anemia might also be present.
Osteoporotic vertebral fracture: Although more common in older individuals, especially postmenopausal women, a vertebral fracture can cause sudden back pain that may radiate to the rib area, especially with movement.