Hi,
I am not diabetic, but because I have a condition were my pancreas does not behave normally, it is possible to have higher than normal readings as you have stated.
However, having diabetes, is diagnosed by fasting levels, Hba1c levels and symptoms.
A pre meal reading or a two hours reading eating moderate carbs, can give you a baseline, and you can measure your response, by having the same meal more than once. Testing is about knowing what your blood glucose levels should be and seeing trends if they differ. Always remember, when testing, a pre meal is important and if you test two hours after first bite, it should not be more than 2mmols than your pre meal reading.