Hi. I doubt beta blockers will have any effect on your sugar levels. I note you are on diamicron (gliclazide in the UK). Any reason why you aren't also on Metformin which most of us start with? It's most useful if you are overweight and insulin resistant. I assume you are on a low-carb diet which many of us find is an essential part of blood sugar control
Read this article and see what it has to say about blood pressure medication and morning highs. If your blood pressure is too well controlled on medication you may need a reduction in you tablets..