Could it happen that a lower back injury cause pain in the abdomen and groin area?

Back pain to groin: Yes. Injury to the back and lower discs may cause pain radiating to the groin/genital region. This is not usually pinched nerve pain, which sends symptoms down the leg and past the knee. So this is called discogenic pain. Rarely, disc problems in the upper lumbar or lower thoracic spine may cause pinched nerve pain to the groin or lower abdomen with associated numbness. Exam is helpful to id.