I've never taken prednisone, but it's a steroid and steroids are well-known for causing hyperglycemia, even in people w/o diabetes. Hyperglycemia is a very common side effect.
I had a similar thing happen two years ago when I had a cortisone shot in my lower back for a herniated disc. My BG was uncontrollable for about 7 days (up in the 300-400 range) after receiving the injection and it seemed like no amount of insulin would bring it down. I will never have one again.
Whether or not you stay on the drug sounds like something you will have to decide- do the benefits of the drug outweight the costs?