I am not a big fan of stretching. I feel that you should be as flexible as you need to be for life or activity. In other words, if you don't do the splits in any part of athletic activity or daily activity, why would you do them period?
As for your back injury, I would not be stretching it like you are. If it gets stiff you may to loosen it up, but I would try and rehab it while I was doing it. Strengthen it. Did you go see a Doctor about the extent of injury? Did he recommend any rehab for it? Are you doing it?
Do you have access to a whirlpool or a sauna? I would say to use that. Another quick and cheap rehab tool for loosening up and getting blood flow to the muscle: Take a hot shower and focus the water on the part that is hurt........after a 10min or so, make the water cold and focus that on the area......do it again a couple of more time. Mel Siff and Dave Tate talk about this increasing blood flow and healing.
I do not know the extent of your injury so I cannot tell you what to do as far as rehabbing it. I can tell you that once it is better, make sure to strengthen your back/hamstrings and abs.
By the way....tight hamstrings are also the cause of a lot of lower back problems.
One last thing....never stretch a cold muscle. You will do more damage then good.