I wouldn't think that it is a stress fracture although this certainly can't be excluded. In most cases, a stress fracture has a very well defined tender spot.
If it is warm, there is definitely inflamed tissue. Therefore, I would not do any strength training or stretching or whatsoever. While the inflammation is there this will only delay the healing.
In your situation, I would continue the NSAID's for some time. Yes, some sources say that they may interfere with the bone growth. Other sources say that you can take them for some time to get rid of the inflammation. And since you don't know whether it is a stress fracture but you can be reasonably sure that there is an inflammation I would go with them.
Diagnosis is not always easy. I am not sure whether you know my story. After a marathon and a 25 km race in the mountains (the famous Dragon-Run) I stopped running in January 2006 due to persistent shin problems. Since they did not go away, I got a bone scan during the summer of 2006. Diagnosis: most likely a stress fracture. Ok, I paused for increasing amounts of time but with no result. In the summer of 2007, I convinced my family doctor to obtain an MRI. Result: no signs of a stress fracture (and they usually see old ones, too) but a mild periostitis (aka shin splints).
How did I get rid of it? I am not sure that I did. At least not completely. After another encounter with the injury, I paused for 3 month. After that I restarted training according to a beginners program (the C25k type). Even with this, I had some setbacks. When I increased the weekly distance, I sometimes felt the injury flaring up again. I learned to back off when this happens. Right now, this works much better (I increased from 12 km in January to 18-20 km per week. This sounds little but is a increase of 50 %. And it is better then no running at all). I am still pretty careful when I increase length or intensity of my workouts and sometimes I still have the impression that there is something. But after such a long time I might just be a little hypersensitive. (Yes, call me a whimp. Gro, Chops, anybody? I prefer to be a running whimp to being a non-running hero). Good luck with your shin KZ.
Follow your nose - Ralf