Sitting back straight is not necessarily the best position for the low
back. The best position seems to be the one that you are most
comfortable with, as simple as that sounds. Changing positions
frequently allows the different structures in the back to unload and
load as needed. Having said that, if you find that the pain in the
middle of your back is increased by sitting slouched, it's often a good
idea to have a back roll to place behind your low back. Your low and
upper back/neck are all connected. If your low back's normal curvature
(lumbar lordosis) is supported in your upright posture with a lumbar
roll, it is often much easier to maintain that upright posture. It is
also worthwhile trying a roll for the neck.  In terms of exercises, I'd
suggest trying standing extension exercises performed slowly every half
hour or so during your sitting job. See if those help at all. In
addition, using a foam roll to place under your middle back and
performing exercises such as the ones mentioned here would help inform
you if your therapist's hunch about posture contributing to your pain
is correct. Here's a link to a good site with foam roll
exercises:http://gymball.com/posture.html  and a couple of posture
correction exercises http://gymball.com/sitting_posture.html
Sometimes, your middle back is stuck into a right or left rotation
position in which case a mobilization or manipulation by a therapist or
a chiropracter might help before you work on your posture.