If you have diabetes, are you also hyperglycemic, hypoglycemic, or both?

Glycemia. Diabetes implies that you are hyperglycemic, by definition.
Yes, but. If fasting for >8 hours fasting sugar 100-125 is pre-diabetes and 2-hrs after eating 140-199 is prediabetes. Fasting 126 and higher and 2 hours after eating 200 and greater is diabetes, that = hyperglycemia some patients with diabetes on therapy with some meds get get low blood sugar, <60, = hypoglycemia see a certified diabetes educator to learn the basics.