Is it normal to have sharp twinges in lower back on right side when sitting or laying down at 37 weeks?

Not unusual: During pregnancy fetus puts mechanical stress on mother's pelvis & three joints of pelvic girdle. An hormone, relaxin, is secreted & loosens ligaments of these joints in preparation for expansion during birthing process; widening birth canal. Lying impresses pelvic ring transferring biomechanical forces to joints of pelvic girdle. Large pelvis sacroiliac joints torque & stretch pained ligaments.