You can definitely get hip pain during labor. In a vaginal birth, the position of delivering your baby requires you to flex at the hip joint. The length of labor can vary, but you may be pushing for two or three hours (or even longer, if you’ve had an epidural). The length of time spent pushing can contribute to pain.
Hip pain may also have to do with the lack of pain coverage from an epidural. This can be addressed by consulting your anesthesiologist again. They can provide solutions to help with the hip pain—and sometimes you may need to consider getting an epidural all over again.