If your back pain didn't start until you began the running program then it is likely that your back and spine cannot handle the compressive forces of running with your extra weight. You may need to begin with something less jarring like walking, biking, running in water, using an elliptical trainer or walking with nordic walking poles. Also, you may need a strengthening program to include your large shock absorbing muscles such as your quads, glutes, abs and back muscles.
However, given that you have symptoms that may require professional help you would be wise to see your doctor &/or physical (physio) therapist. A therapist could evaluate your muscle imbalances (like tight hamstrings and hip flexors as well as muscle weaknesses), and give you specific corrective exercises. They will also keep you from doing inappropriate exercises that may make your condition worse. They could also evaluate your running form and make recommendations as to how to proceed so that you can safely exercise to lose weight.
The biggest mistake would be to continue to aggravate your back condition and slow your progress all together. Trying to do exercises that are not appropriate for your specific back condition can lead to a chronic problem.
As for prolonged sitting, the key is to get up and move every half hour or so (easier said than done). A towel or sweater rolled in the small of your back may help.
And don't overlook your diet which is key to losing weight. Good luck.