Congratulations on your successful liver transplant [LTP]. I am going on 5.6 years LTP and understand your puzzlement as I had the same. First, let's review your main medications. Then I'll give you some suggestions to help control and manage your glucose [blood sugar] levels. And to answer your subject question, yes there are medicinal induced diseases, diabetes type 2 being one. I for one can attest to that.
Wysolone is a cousin to Prednisolone and helps to reduce your liver inflamation [swelling]. It's also used to treat animal [dogs and cats] problems. The bad thing is it's classified as steroid. The more you take, the higher it will raise your glucose levels. The longer you take it, the higher the risk of constant elevated glucose. Depending on how well your post OP recovery goes, you probably will be weaned off of Prednisolone. Whether or not permanent diabetes occurs is hard to say, as each patient is different.
PanGraf is a cousin to Prograf [Tacrolimus] one of your immunosupressants [Cellcept being the other]. Prograf has a 20% chance of raising glucose levels. I, for one, am in that 20 percentile, while others I know are not.
Has been known to raise glucose levels. Again, depends on each patient.
What should you do?
I know after the OP you feel so-o-o much better but do not over stress your body. It takes a long time for the insides to heal. Now is the time to carefully monitor your nutrition. Not everyone is the same. What a dozen other TP'ers can eat may not apply to you. Same as what diabetes forum members or web sites claim as being safe to eat may not be good for you.
Start a food log, a dairy of everything you eat and drink including portion size. Test your glucose just before a meal and 2-3 hours after a meal. Before will give you a baseline, the 2-3 hours after is two fold; 1. This is when glucose from the foods you ate are peaking in your blood stream; 2. It tells you what foods are raising your glucose above normal and those that do not. Avoid and do not eat foods that do, plain and simple.
Good luck. Take it easy during your first year, let your body heal. After that, resume normal activities. And understand one thing, you body never fully adjusts to the new liver. That's why you are going to eat immunosuppressants for the rest of your life.