Tiger, I think that it's worth discussing with your doctors about the type of diabetes they think you have and the contribution of the prednislone.
This is what I think may have happened but I may be wrong so please ask your doctors again.
First you have had diabetes for some time. You have to take a steroid which makes it difficult for you to keep you glucose levels down. This has resulted in your beta cells not being able to produce enough insulin.
When you went into hospital you had very high glucose levels and ketones.The ketones were produced because the the high glucose levels combined with insufficient insulin meant your body started to use it's fat for energy. (this is what produces the ketones and weight loss)
The high glucose and ketones were toxic to your bod and your beta cells which produce insulin, were not up to the task and to put it simply 'gave up'.
In hospital they gave you fairly large amounts of insulin to lower the blood glucose and also to get rid of the ketones. ( I would need to take quite a bit of extra insulin for levels above 14mmol with ketones)
0nce your glucose levels had got back to nearer normal levels, your remaining beta cell were able to produce some insulin again, though (possibly) not enough for you to manage without injected insulin.