Take this with a huge grain of salt because I'm not completely sure. :P
For a good strong posture you need abdominal muscle strength. It's something I've picked up as a runner where big strong back does more bad than good if you want be good at running.
Sounds more like you need to support you arms better at your desk. I got back strains working as an electrician because most of the day is spent working with unsupported arms/hands.