Hi smiley and welcome to the forum, almost certainly the pred is causing your high bg levels between meals, I was diagnosed T2 having been on pred for 2 years plus and had to be put straight on mdi treatment, thats 'multiple daily injections' of insulin so I was taking a long acting insulin at night to keep my bg levels stable between meals as well as a short acting insulin before meals to deal with the glucose produced from my meals.
I would hazard a guess that the reason your bg levels are rising and staying high is because you need a long acting basal (base level) insulin to flaten out your levels between meals, but I am NOT A DOCTOR so I would advise you to talk to your doctor/consultant and explain what you have experienced and perhaps ask about the possibility of a long acting (basal) insulin being added to your meds.
It is well known that corticosteroids raise bg levels and long term users like myself are known to be at risk of developing T2 diabetes and thats exactly what happened to me.
Reducing the carbs in your diet will help to a degree but you will almost certainly require medication to fully control your bg levels while you are using prednisolone for any length of time more than a few odd days or weeks here and there.
I was on prednisolone for just over 3 years in total and thankfully have not had to resort to it again (in 5 years) fingers crossed, it probably saved my life though so I cant complain.
So see your doctor/consultant and good luck
