When you say "dizziness that won't go away," do you mean that literally - that you are dizzy almost all the time? Or is it intermittent dizziness? If intermittent, then how often and under what circumstances?
One type of intermittent dizziness that was not mentioned above is postprandial hypotension - low blood pressure after eating. I have high blood pressure normally. In fact, I'm on three BP medications to control it. But since my BP typically drops 20-40 points after I eat, I have to be careful not to have my meds adjusted too much, or I'll get dizzy after meals. Yesterday I even dropped more than 50 points after one meal. I don't know what age you are, but postprandial hypotension is almost unknown in people in their 20s. By age 65, though, some sources say that as many as 30% of people have it.
This, too, is not diabetes related.