I was told a long time ago that I have compacted vertebra

A compacted vertebrae could be the result of a crush fracture in the past.  You may or may not remember an injury of some kind in the past which could have caused this - an impact type injury or a fall are possibilities. If the injury is old it is likely that the bony vertebrae is well healed although you may have lost a little height and movement of that particular vertebrae.  Provided you keep good posture and strong core stability of the back and pelvic areas you are much less likely to experience problems associated with this damaged vertebrae.  Pilates style core strengthening exercises are an excellent way to develop good posture and back strength but I would advise consulting with a qualified instructor so that you can be shown how to do these exercises correctly as poor technique can do more harm than good.