If you are still working is there any way that you can not sit for so long? Perhaps you can stand for some calls or get up and walk around between calls or at least every half hour or so, Sitting tends to shorten your muscles and this muscle tension causes pain. If you can put a small stool or something under your feet while sitting, this will also help.
Also the 45 minutes of exercise may be too much, especially as you are pushing through the pain. Perhaps time yourself to see how long you can exercise before the pain comes,and then do less than that for a week or so and very gradually build it up. The latest neuroscience findings on pain show that the brain plays a great part in determining how much pain you feel, and that if you push through pain the threshold for pain tolerance is reduced (I'm not saying it's all in your head, just that the brain determines when something is 'dangerous' based on past experience.) When I initially had my chronic pain I could only walk for a 90 seconds on land before the pain got so bad I had to stop. On the advice of my hydrotherapist I cut walking time for to 45 seconds, did that for a week and then gradually built the time up again by increasing it by 10% a week. It took a long time but now I can walk as far as I want without pain.
Another thing you might want to try is hydrotherapy. It's much easier than exercising on land because the buoyancy of the water reduces your body weight and the resistance of the water increases muscle strength, You do need to do it with a therapist initially so they can show you what to do and make sure you don;t overdo it. You not only need to strengthen your back muscles, but also the core muscles in your abdomen, since they take much of the strain off your back. I found it to be the best thing in getting strong again.
Finally, although you seem to be bearing up extraordinarily well considering what you are going through, you are probably quite (or very) stressed, Stress causes, or worsens pain so if you could reduce stress by meditating or using another stress reduction technique, it would be helpful. An easy way of meditating is Dr. Herbert Benson's Relaxation Response. Basically you sit comfortably, close your eyes and each time you breathe out say 'one'. If thoughts come up don't get entangled with them, just say to yourself 'Oh well' and return to focusing on your breathing. Do this for ten to twenty minutes twice a day, and your stress will decrease. Also try and do something you love each day because that will also help relieve your stress.
And do everything you can to get a good nights sleep.