Hi there. When thirst is described as a symptom of diabetes (mellitus), it is probably a daily feeling. This happens when the person has uncontrolled blood sugar, really very high. From what you have written in your posts, it seems your blood sugar is not uncontrolled. This is why I don't think your thirst is related to diabetes (mellitus).
The articles I read online say thirst is also a symptom of diabetes insipidus but this is why you need lab tests to find out what's going on. If your blood sugar is ok, then it must be something else. Diabetes insipidus affects the kidneys.